10:52 a.m.
Hi all,
Just a general VAR related question. When is it appropriate to include
a deterministic time trend in the reduced form VAR? Visually some of the
data series (not all) look like they have trending properties. In any case,
does the inclusion of the time trend matter if the process is stable and
therefore stationary (i.e. the polynomial defined by the determinant of the
autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better
way to test whether the underlying data generating process has a stochastic
or deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
2:17 p.m.
MJ,
If your data have deterministic trends, then unit root tests should pick that up (though
there may be a problem in small samples). If you include a trend but the dgp is
stationary, then a t-test should conclude that the trend coefficient is zero. Presumably
your unit root tests reject the null, right?
From: gretl-users-bounces(a)lists.wfu.edu [mailto:gretl-users-bounces@lists.wfu.edu] On
Behalf Of Muheed Jamaldeen
Sent: Monday, December 12, 2011 5:52 AM
To: Gretl list
Subject: [Gretl-users] Deterministic trend in VAR
Hi all,
Just a general VAR related question. When is it appropriate to include a deterministic
time trend in the reduced form VAR? Visually some of the data series (not all) look like
they have trending properties. In any case, does the inclusion of the time trend matter if
the process is stable and therefore stationary (i.e. the polynomial defined by the
determinant of the autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better way to test
whether the underlying data generating process has a stochastic or deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
11:59 p.m.
Peter,
I have 100 observations in the model. So small samples may or may not be an
issue. I am wondering if the deterministic trend is an issue at all because
the VAR is stable implying stationarity of the described process in each
equation WITHOUT the trend (i.e. the polynomial defined by the determinant
of the autoregressive operator has no roots in and on the complex unit
circle without the time trend term).
The ADF tests suggest that we cannot reject the trend term. Let me show you
an example. Following is the ADF tests for logged US GDP.
Monte Carlo studies suggest that choosing the lag order (p) of the unit
root tests according to the formula: Int {12(*T */100)1/ 4} so the lag
order is 12 with 100 observations.
test without constant
test statistic: tau_nc(1) = 2.13551
asymptotic p-value 0.9927
test with constant
test statistic: tau_c(1) = -1.28148
asymptotic p-value 0.6405
with constant and trend
test statistic: tau_ct(1) = -0.728436
asymptotic p-value 0.9702
Following is the estimate for the trend term in the last ADF regression.
coefficient std. error t-ratio p-value
-------------------------------------------------------------
time 0.000200838 0.000317669 0.6322 0.5292
So all three tests are saying that I cannot reject the null of unit root.
Including I(1) variables in an unrestricted VAR is fine as Lutekepohl and
Toda and Yammoto have demonstrated. It's a question of whether a trend term
is to be included. I am inclined to think not because the VAR is stable
WITHOUT a trend.
Thoughts?
Cheers,
Mj
On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter <psummers(a)highpoint.edu>wrote:
MJ,****
** **
If your data have deterministic trends, then unit root tests should pick
that up (though there may be a problem in small samples). If you include a
trend but the dgp is stationary, then a t-test should conclude that the
trend coefficient is zero. Presumably your unit root tests reject the null,
right? ****
** **
*From:* gretl-users-bounces(a)lists.wfu.edu [mailto:
gretl-users-bounces(a)lists.wfu.edu] *On Behalf Of *Muheed Jamaldeen
*Sent:* Monday, December 12, 2011 5:52 AM
*To:* Gretl list
*Subject:* [Gretl-users] Deterministic trend in VAR****
** **
Hi all,****
Just a general VAR related question. When is it appropriate to include
a deterministic time trend in the reduced form VAR? Visually some of the
data series (not all) look like they have trending properties. In any case,
does the inclusion of the time trend matter if the process is stable and
therefore stationary (i.e. the polynomial defined by the determinant of the
autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better
way to test whether the underlying data generating process has a stochastic
or deterministic process?****
** **
I am mainly interested in the impulse responses. ****
** **
Cheers,****
** **
Mj****
** **
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
12:46 a.m.
MJ,
You're right that the unit root tests are telling you that you have a unit root in at
least one series.
I'm confused about what your VAR looks like though (and maybe the rest of the list is
too). If this is one of the series in your VAR, then it's not stable/stationary, by
definition. That is, the lag operator polynomial will have at least one root on the unit
circle. My earlier answer assumed that your unit root & cointegration tests ruled out
both, but now it seems that's not the case.
Relating to ths, how many series do you have in your VAR? My feeling is that 100 obs per
series isn't really a lot, especially if you're trying to sort out issues related
to deterministic vs stochastic trends, cointegration vs none, etc.
At this point I'd suggest a) reading the gretl manual and/or your favorite reference
on VARs & VECMs, and/or b) providing some more detail about what you're trying to
do.
PS
________________________________
From: gretl-users-bounces(a)lists.wfu.edu [gretl-users-bounces(a)lists.wfu.edu] on behalf of
Muheed Jamaldeen [mj.myworld(a)gmail.com]
Sent: Monday, December 12, 2011 6:59 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Peter,
I have 100 observations in the model. So small samples may or may not be an issue. I am
wondering if the deterministic trend is an issue at all because the VAR is stable implying
stationarity of the described process in each equation WITHOUT the trend (i.e. the
polynomial defined by the determinant of the autoregressive operator has no roots in and
on the complex unit circle without the time trend term).
The ADF tests suggest that we cannot reject the trend term. Let me show you an example.
Following is the ADF tests for logged US GDP.
Monte Carlo studies suggest that choosing the lag order (p) of the unit root tests
according to the formula: Int {12(T /100)1/ 4} so the lag order is 12 with 100
observations.
test without constant
test statistic: tau_nc(1) = 2.13551
asymptotic p-value 0.9927
test with constant
test statistic: tau_c(1) = -1.28148
asymptotic p-value 0.6405
with constant and trend
test statistic: tau_ct(1) = -0.728436
asymptotic p-value 0.9702
Following is the estimate for the trend term in the last ADF regression.
coefficient std. error t-ratio p-value
-------------------------------------------------------------
time 0.000200838 0.000317669 0.6322 0.5292
So all three tests are saying that I cannot reject the null of unit root. Including I(1)
variables in an unrestricted VAR is fine as Lutekepohl and Toda and Yammoto have
demonstrated. It's a question of whether a trend term is to be included. I am inclined
to think not because the VAR is stable WITHOUT a trend.
Thoughts?
Cheers,
Mj
On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter
<psummers@highpoint.edu<mailto:psummers@highpoint.edu>> wrote:
MJ,
If your data have deterministic trends, then unit root tests should pick that up (though
there may be a problem in small samples). If you include a trend but the dgp is
stationary, then a t-test should conclude that the trend coefficient is zero. Presumably
your unit root tests reject the null, right?
From: gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>
[mailto:gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>]
On Behalf Of Muheed Jamaldeen
Sent: Monday, December 12, 2011 5:52 AM
To: Gretl list
Subject: [Gretl-users] Deterministic trend in VAR
Hi all,
Just a general VAR related question. When is it appropriate to include a deterministic
time trend in the reduced form VAR? Visually some of the data series (not all) look like
they have trending properties. In any case, does the inclusion of the time trend matter if
the process is stable and therefore stationary (i.e. the polynomial defined by the
determinant of the autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better way to test
whether the underlying data generating process has a stochastic or deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
http://lists.wfu.edu/mailman/listinfo/gretl-users
12:59 a.m.
You're right about the VAR not being stable if USGDP were the only series
in the model. Well, the VAR is a 11 variable VAR (4). The 11 variables are
GDP and macroeconomic variables.
I am testing the impact of cash rate innovations on GDP. The question is,
if the reduced form is stable (and stationary) WITHOUT a trend, should one
include a trend when the univariate tests suggest that SOME of the series
may have trend in their unit roots.
Hope that makes sense?
On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter <psummers(a)highpoint.edu>wrote:
MJ,
You're right that the unit root tests are telling you that you have a unit
root in at least one series.
I'm confused about what your VAR looks like though (and maybe the rest of
the list is too). If this is one of the series in your VAR, then it's not
stable/stationary, by definition. That is, the lag operator polynomial will
have at least one root on the unit circle. My earlier answer assumed that
your unit root & cointegration tests ruled out both, but now it seems
that's not the case.
Relating to ths, how many series do you have in your VAR? My feeling is
that 100 obs per series isn't really a lot, especially if you're trying to
sort out issues related to deterministic vs stochastic trends,
cointegration vs none, etc.
At this point I'd suggest a) reading the gretl manual and/or your favorite
reference on VARs & VECMs, and/or b) providing some more detail about what
you're trying to do.
PS
________________________________
From: gretl-users-bounces(a)lists.wfu.edu [gretl-users-bounces(a)lists.wfu.edu]
on behalf of Muheed Jamaldeen [mj.myworld(a)gmail.com]
Sent: Monday, December 12, 2011 6:59 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Peter,
I have 100 observations in the model. So small samples may or may not be
an issue. I am wondering if the deterministic trend is an issue at all
because the VAR is stable implying stationarity of the described process in
each equation WITHOUT the trend (i.e. the polynomial defined by the
determinant of the autoregressive operator has no roots in and on the
complex unit circle without the time trend term).
The ADF tests suggest that we cannot reject the trend term. Let me show
you an example. Following is the ADF tests for logged US GDP.
Monte Carlo studies suggest that choosing the lag order (p) of the unit
root tests according to the formula: Int {12(T /100)1/ 4} so the lag order
is 12 with 100 observations.
test without constant
test statistic: tau_nc(1) = 2.13551
asymptotic p-value 0.9927
test with constant
test statistic: tau_c(1) = -1.28148
asymptotic p-value 0.6405
with constant and trend
test statistic: tau_ct(1) = -0.728436
asymptotic p-value 0.9702
Following is the estimate for the trend term in the last ADF regression.
coefficient std. error t-ratio p-value
-------------------------------------------------------------
time 0.000200838 0.000317669 0.6322 0.5292
So all three tests are saying that I cannot reject the null of unit root.
Including I(1) variables in an unrestricted VAR is fine as Lutekepohl and
Toda and Yammoto have demonstrated. It's a question of whether a trend term
is to be included. I am inclined to think not because the VAR is stable
WITHOUT a trend.
Thoughts?
Cheers,
Mj
On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter <psummers(a)highpoint.edu
<mailto:psummers@highpoint.edu>> wrote:
MJ,
If your data have deterministic trends, then unit root tests should pick
that up (though there may be a problem in small samples). If you include a
trend but the dgp is stationary, then a t-test should conclude that the
trend coefficient is zero. Presumably your unit root tests reject the null,
right?
From: gretl-users-bounces(a)lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu> [mailto:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>]
On Behalf Of Muheed Jamaldeen
Sent: Monday, December 12, 2011 5:52 AM
To: Gretl list
Subject: [Gretl-users] Deterministic trend in VAR
Hi all,
Just a general VAR related question. When is it appropriate to include a
deterministic time trend in the reduced form VAR? Visually some of the data
series (not all) look like they have trending properties. In any case, does
the inclusion of the time trend matter if the process is stable and
therefore stationary (i.e. the polynomial defined by the determinant of the
autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better
way to test whether the underlying data generating process has a stochastic
or deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
http://lists.wfu.edu/mailman/listinfo/gretl-users
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
1:28 a.m.
Greetings all
Have to say I'm getting confused, here.
I'd be appreciative please if somebody would tell me please
what this means "the reduced form".... of what?
Also if a set is stable as you say, and to produce its stationarity you are confident that
you haven't
squelched out important information from the data by differencing etc, what's the
reason to introduce trend information and then trust inferences from the results ?
Trend in their Unit Roots?
I'm cool
rest easy
Richard Hudson
Dr RJF Hudson Qld Australia
rjfhud(a)powerup.com.au
----- Original Message -----
From: Muheed Jamaldeen
To: Gretl list
Sent: Tuesday, December 13, 2011 10:59 AM
Subject: Re: [Gretl-users] Deterministic trend in VAR
You're right about the VAR not being stable if USGDP were the only series in the
model. Well, the VAR is a 11 variable VAR (4). The 11 variables are GDP and macroeconomic
variables.
I am testing the impact of cash rate innovations on GDP. The question is, if the reduced
form is stable (and stationary) WITHOUT a trend, should one include a trend when the
univariate tests suggest that SOME of the series may have trend in their unit roots.
Hope that makes sense?
On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter <psummers(a)highpoint.edu> wrote:
MJ,
You're right that the unit root tests are telling you that you have a unit root in
at least one series.
I'm confused about what your VAR looks like though (and maybe the rest of the list
is too). If this is one of the series in your VAR, then it's not stable/stationary, by
definition. That is, the lag operator polynomial will have at least one root on the unit
circle. My earlier answer assumed that your unit root & cointegration tests ruled out
both, but now it seems that's not the case.
Relating to ths, how many series do you have in your VAR? My feeling is that 100 obs
per series isn't really a lot, especially if you're trying to sort out issues
related to deterministic vs stochastic trends, cointegration vs none, etc.
At this point I'd suggest a) reading the gretl manual and/or your favorite
reference on VARs & VECMs, and/or b) providing some more detail about what you're
trying to do.
PS
________________________________
From: gretl-users-bounces(a)lists.wfu.edu [gretl-users-bounces(a)lists.wfu.edu] on behalf
of Muheed Jamaldeen [mj.myworld(a)gmail.com]
Sent: Monday, December 12, 2011 6:59 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Peter,
I have 100 observations in the model. So small samples may or may not be an issue. I
am wondering if the deterministic trend is an issue at all because the VAR is stable
implying stationarity of the described process in each equation WITHOUT the trend (i.e.
the polynomial defined by the determinant of the autoregressive operator has no roots in
and on the complex unit circle without the time trend term).
The ADF tests suggest that we cannot reject the trend term. Let me show you an
example. Following is the ADF tests for logged US GDP.
Monte Carlo studies suggest that choosing the lag order (p) of the unit root tests
according to the formula: Int {12(T /100)1/ 4} so the lag order is 12 with 100
observations.
test without constant
test statistic: tau_nc(1) = 2.13551
asymptotic p-value 0.9927
test with constant
test statistic: tau_c(1) = -1.28148
asymptotic p-value 0.6405
with constant and trend
test statistic: tau_ct(1) = -0.728436
asymptotic p-value 0.9702
Following is the estimate for the trend term in the last ADF regression.
coefficient std. error t-ratio p-value
-------------------------------------------------------------
time 0.000200838 0.000317669 0.6322 0.5292
So all three tests are saying that I cannot reject the null of unit root. Including
I(1) variables in an unrestricted VAR is fine as Lutekepohl and Toda and Yammoto have
demonstrated. It's a question of whether a trend term is to be included. I am inclined
to think not because the VAR is stable WITHOUT a trend.
Thoughts?
Cheers,
Mj
On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter
<psummers@highpoint.edu<mailto:psummers@highpoint.edu>> wrote:
MJ,
If your data have deterministic trends, then unit root tests should pick that up
(though there may be a problem in small samples). If you include a trend but the dgp is
stationary, then a t-test should conclude that the trend coefficient is zero. Presumably
your unit root tests reject the null, right?
From:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>
[mailto:gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>]
On Behalf Of Muheed Jamaldeen
Sent: Monday, December 12, 2011 5:52 AM
To: Gretl list
Subject: [Gretl-users] Deterministic trend in VAR
Hi all,
Just a general VAR related question. When is it appropriate to include a deterministic
time trend in the reduced form VAR? Visually some of the data series (not all) look like
they have trending properties. In any case, does the inclusion of the time trend matter if
the process is stable and therefore stationary (i.e. the polynomial defined by the
determinant of the autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better way to test
whether the underlying data generating process has a stochastic or deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
http://lists.wfu.edu/mailman/listinfo/gretl-users
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
------------------------------------------------------------------------------
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
1:44 a.m.
Sorry about the lack of clarity at times. lol.
Reduced form = reduced form (yt as a function of all past values of system)
VAR (VectorAutoRegression)
Trend in the unit root = including a deterministic trend term in the ADF
equation for unit roots.
Hope that makes sense.
Well, the stability of the reduced form (VAR) is achieved without adding a
trend term to each variables equation. There is no differencing involved.
Estimation is in levels.
On Tue, Dec 13, 2011 at 12:28 PM, Dr RJF Hudson <rjfhud(a)powerup.com.au>wrote:
**
Greetings all
Have to say I'm getting confused, here.
I'd be appreciative please if somebody would tell me please
what this means "the reduced form".... of what?
Also if a set is stable as you say, and to produce its stationarity you
are confident that you haven't
squelched out important information from the data by differencing
etc, what's the reason to introduce trend information and then trust
inferences from the results ?
Trend in their Unit Roots?
I'm cool
rest easy
Richard Hudson
Dr RJF Hudson Qld Australia
rjfhud(a)powerup.com.au
----- Original Message -----
*From:* Muheed Jamaldeen <mj.myworld(a)gmail.com>
*To:* Gretl list <gretl-users(a)lists.wfu.edu>
*Sent:* Tuesday, December 13, 2011 10:59 AM
*Subject:* Re: [Gretl-users] Deterministic trend in VAR
You're right about the VAR not being stable if USGDP were the only series
in the model. Well, the VAR is a 11 variable VAR (4). The 11 variables are
GDP and macroeconomic variables.
I am testing the impact of cash rate innovations on GDP. The question is,
if the reduced form is stable (and stationary) WITHOUT a trend, should one
include a trend when the univariate tests suggest that SOME of the series
may have trend in their unit roots.
Hope that makes sense?
On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter <psummers(a)highpoint.edu>wrote:
> MJ,
>
> You're right that the unit root tests are telling you that you have a
> unit root in at least one series.
>
> I'm confused about what your VAR looks like though (and maybe the rest of
> the list is too). If this is one of the series in your VAR, then it's not
> stable/stationary, by definition. That is, the lag operator polynomial will
> have at least one root on the unit circle. My earlier answer assumed that
> your unit root & cointegration tests ruled out both, but now it seems
> that's not the case.
>
> Relating to ths, how many series do you have in your VAR? My feeling is
> that 100 obs per series isn't really a lot, especially if you're trying to
> sort out issues related to deterministic vs stochastic trends,
> cointegration vs none, etc.
>
> At this point I'd suggest a) reading the gretl manual and/or your
> favorite reference on VARs & VECMs, and/or b) providing some more detail
> about what you're trying to do.
>
> PS
> ________________________________
> From: gretl-users-bounces(a)lists.wfu.edu [
> gretl-users-bounces(a)lists.wfu.edu] on behalf of Muheed Jamaldeen [
> mj.myworld(a)gmail.com]
> Sent: Monday, December 12, 2011 6:59 PM
> To: Gretl list
> Subject: Re: [Gretl-users] Deterministic trend in VAR
>
> Peter,
>
> I have 100 observations in the model. So small samples may or may not be
> an issue. I am wondering if the deterministic trend is an issue at all
> because the VAR is stable implying stationarity of the described process in
> each equation WITHOUT the trend (i.e. the polynomial defined by the
> determinant of the autoregressive operator has no roots in and on the
> complex unit circle without the time trend term).
>
> The ADF tests suggest that we cannot reject the trend term. Let me show
> you an example. Following is the ADF tests for logged US GDP.
>
> Monte Carlo studies suggest that choosing the lag order (p) of the unit
> root tests according to the formula: Int {12(T /100)1/ 4} so the lag order
> is 12 with 100 observations.
>
> test without constant
> test statistic: tau_nc(1) = 2.13551
> asymptotic p-value 0.9927
>
> test with constant
> test statistic: tau_c(1) = -1.28148
> asymptotic p-value 0.6405
>
> with constant and trend
> test statistic: tau_ct(1) = -0.728436
> asymptotic p-value 0.9702
>
> Following is the estimate for the trend term in the last ADF regression.
>
> coefficient std. error t-ratio
> p-value
> -------------------------------------------------------------
> time 0.000200838 0.000317669 0.6322 0.5292
>
> So all three tests are saying that I cannot reject the null of unit root.
> Including I(1) variables in an unrestricted VAR is fine as Lutekepohl and
> Toda and Yammoto have demonstrated. It's a question of whether a trend term
> is to be included. I am inclined to think not because the VAR is stable
> WITHOUT a trend.
>
> Thoughts?
>
> Cheers,
>
> Mj
>
> On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter <psummers(a)highpoint.edu
> <mailto:psummers@highpoint.edu>> wrote:
> MJ,
>
> If your data have deterministic trends, then unit root tests should pick
> that up (though there may be a problem in small samples). If you include a
> trend but the dgp is stationary, then a t-test should conclude that the
> trend coefficient is zero. Presumably your unit root tests reject the null,
> right?
>
> From: gretl-users-bounces(a)lists.wfu.edu<mailto:
> gretl-users-bounces(a)lists.wfu.edu> [mailto:
> gretl-users-bounces(a)lists.wfu.edu<mailto:
> gretl-users-bounces(a)lists.wfu.edu>] On Behalf Of Muheed Jamaldeen
> Sent: Monday, December 12, 2011 5:52 AM
> To: Gretl list
> Subject: [Gretl-users] Deterministic trend in VAR
>
> Hi all,
> Just a general VAR related question. When is it appropriate to include a
> deterministic time trend in the reduced form VAR? Visually some of the data
> series (not all) look like they have trending properties. In any case, does
> the inclusion of the time trend matter if the process is stable and
> therefore stationary (i.e. the polynomial defined by the determinant of the
> autoregressive operator has no roots in and on the complex unit circle)
> without the time trend term. Other than unit root tests, is there a better
> way to test whether the underlying data generating process has a stochastic
> or deterministic process?
>
> I am mainly interested in the impulse responses.
>
> Cheers,
>
> Mj
>
>
> _______________________________________________
> Gretl-users mailing list
> Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
>
> _______________________________________________
> Gretl-users mailing list
> Gretl-users(a)lists.wfu.edu
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
------------------------------
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
1:51 a.m.
I'm confused too.
MJ, is the (log) level of GDP one of the 11 series in your VAR? If so, then based on the
unit root tests you showed earlier, it is not "stable (and stationary) without a
trend." On the contrary, it has a unit root -- and is therefore non-stationary --
whether or not a deterministic trend is included in the dgp.
In other words, including the level of GDP in your reduced-form VAR renders it
non-stationary.
Back to the potential small-sample issue: a VAR with 11 variables and 4 lags has 44
parameters per equation, not counting a constant (or trend?!). There are also 55
parameters in the covariance matrix. With 100 observations per series, you're asking
quite a lot of your data set. Even if you knew the covariance matrix for sure, you'd
have just over 2 obs/parameter for estimating the dynamics. I don't think that's
asymptotic yet, but I could be wrong ;-)
________________________________
From: gretl-users-bounces(a)lists.wfu.edu [gretl-users-bounces(a)lists.wfu.edu] on behalf of
Dr RJF Hudson [rjfhud(a)powerup.com.au]
Sent: Monday, December 12, 2011 8:28 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Greetings all
Have to say I'm getting confused, here.
I'd be appreciative please if somebody would tell me please
what this means "the reduced form".... of what?
Also if a set is stable as you say, and to produce its stationarity you are confident that
you haven't
squelched out important information from the data by differencing etc, what's the
reason to introduce trend information and then trust inferences from the results ?
Trend in their Unit Roots?
I'm cool
rest easy
Richard Hudson
Dr RJF Hudson Qld Australia
rjfhud@powerup.com.au<mailto:rjfhud@powerup.com.au>
----- Original Message -----
From: Muheed Jamaldeen<mailto:mj.myworld@gmail.com>
To: Gretl list<mailto:gretl-users@lists.wfu.edu>
Sent: Tuesday, December 13, 2011 10:59 AM
Subject: Re: [Gretl-users] Deterministic trend in VAR
You're right about the VAR not being stable if USGDP were the only series in the
model. Well, the VAR is a 11 variable VAR (4). The 11 variables are GDP and macroeconomic
variables.
I am testing the impact of cash rate innovations on GDP. The question is, if the reduced
form is stable (and stationary) WITHOUT a trend, should one include a trend when the
univariate tests suggest that SOME of the series may have trend in their unit roots.
Hope that makes sense?
On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter
<psummers@highpoint.edu<mailto:psummers@highpoint.edu>> wrote:
MJ,
You're right that the unit root tests are telling you that you have a unit root in at
least one series.
I'm confused about what your VAR looks like though (and maybe the rest of the list is
too). If this is one of the series in your VAR, then it's not stable/stationary, by
definition. That is, the lag operator polynomial will have at least one root on the unit
circle. My earlier answer assumed that your unit root & cointegration tests ruled out
both, but now it seems that's not the case.
Relating to ths, how many series do you have in your VAR? My feeling is that 100 obs per
series isn't really a lot, especially if you're trying to sort out issues related
to deterministic vs stochastic trends, cointegration vs none, etc.
At this point I'd suggest a) reading the gretl manual and/or your favorite reference
on VARs & VECMs, and/or b) providing some more detail about what you're trying to
do.
PS
________________________________
From: gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>
[gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>] on
behalf of Muheed Jamaldeen [mj.myworld@gmail.com<mailto:mj.myworld@gmail.com>]
Sent: Monday, December 12, 2011 6:59 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Peter,
I have 100 observations in the model. So small samples may or may not be an issue. I am
wondering if the deterministic trend is an issue at all because the VAR is stable implying
stationarity of the described process in each equation WITHOUT the trend (i.e. the
polynomial defined by the determinant of the autoregressive operator has no roots in and
on the complex unit circle without the time trend term).
The ADF tests suggest that we cannot reject the trend term. Let me show you an example.
Following is the ADF tests for logged US GDP.
Monte Carlo studies suggest that choosing the lag order (p) of the unit root tests
according to the formula: Int {12(T /100)1/ 4} so the lag order is 12 with 100
observations.
test without constant
test statistic: tau_nc(1) = 2.13551
asymptotic p-value 0.9927
test with constant
test statistic: tau_c(1) = -1.28148
asymptotic p-value 0.6405
with constant and trend
test statistic: tau_ct(1) = -0.728436
asymptotic p-value 0.9702
Following is the estimate for the trend term in the last ADF regression.
coefficient std. error t-ratio p-value
-------------------------------------------------------------
time 0.000200838 0.000317669 0.6322 0.5292
So all three tests are saying that I cannot reject the null of unit root. Including I(1)
variables in an unrestricted VAR is fine as Lutekepohl and Toda and Yammoto have
demonstrated. It's a question of whether a trend term is to be included. I am inclined
to think not because the VAR is stable WITHOUT a trend.
Thoughts?
Cheers,
Mj
On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter
<psummers@highpoint.edu<mailto:psummers@highpoint.edu><mailto:psummers@highpoint.edu<mailto:psummers@highpoint.edu>>>
wrote:
MJ,
If your data have deterministic trends, then unit root tests should pick that up (though
there may be a problem in small samples). If you include a trend but the dgp is
stationary, then a t-test should conclude that the trend coefficient is zero. Presumably
your unit root tests reject the null, right?
From:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu><mailto:gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>>
[mailto:gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu><mailto:gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>>]
On Behalf Of Muheed Jamaldeen
Sent: Monday, December 12, 2011 5:52 AM
To: Gretl list
Subject: [Gretl-users] Deterministic trend in VAR
Hi all,
Just a general VAR related question. When is it appropriate to include a deterministic
time trend in the reduced form VAR? Visually some of the data series (not all) look like
they have trending properties. In any case, does the inclusion of the time trend matter if
the process is stable and therefore stationary (i.e. the polynomial defined by the
determinant of the autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better way to test
whether the underlying data generating process has a stochastic or deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu><mailto:Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>>
http://lists.wfu.edu/mailman/listinfo/gretl-users
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
http://lists.wfu.edu/mailman/listinfo/gretl-users
________________________________
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
2:33 a.m.
Hi Peter,
Yes. USGDP is part of the 11 variables. I didn't want to clutter the list
with the rest of the tests and other information.
I am estimating the reduced form (near) VAR and SVAR on JMULTI whilst using
Gretl for preliminary testing. JMULTI computes modulus of the eigenvalues
of the reverse characteristic polynomial which are all greater than one
(which is the stability condition, implying stationarity).
Let me explain what I mean by stability implying stationarity using
Lutekepohl's text:
" The process is stable if det(IK − A1z − ·· ·− Apz p) = 0 for |z| ≤ 1,
(3.2) that is, the polynomial defined by the determinant of the
autoregressive operator has no roots in and on the complex unit circle. On
the assumption that the process has been initiated in the infinite past (t
= 0,±1,±2, . . .), it generates stationary time series that have
time-invariant means, variances, and covariance structure."
He makes a similar argument here:
http://books.google.com.au/books?id=muorJ6FHIiEC&q=Stable#v=snippet&a...
See the proposition in page 25.
That makes sense to me because regardless of what the univariate Data
Generating Process (DGP) suggests, the description of the process by each
VAR equation is stable, implying stationarity. If this is WITHOUT a trend
term, then is there a case for a trend term? That is the crux of the
question. The distinction is that the DGP may not be stationary, but the
VAR process is. So there is no problem if the VAR process is stable (and
thereby stationary) without a trend term.
I agree with your small sample point. But my hands are tied there! lol.
Also, for consistency I computed the VAR inverse roots on Gretl. They are
all inside the unit circle. Implying stability of the VAR process.
roots (real, imaginary, modulus, frequency)
1: (-0.6179, 0.4963, 0.7925, 0.3923)
2: (-0.6179, -0.4963, 0.7925, -0.3923)
3: (-0.7550, 0.0000, 0.7550, 0.5000)
4: (-0.7032, 0.1521, 0.7195, 0.4661)
5: (-0.7032, -0.1521, 0.7195, -0.4661)
6: (-0.4947, 0.6105, 0.7857, 0.3584)
7: (-0.4947, -0.6105, 0.7857, -0.3584)
8: (-0.5062, 0.3974, 0.6435, 0.3941)
9: (-0.5062, -0.3974, 0.6435, -0.3941)
10: (-0.5245, 0.2641, 0.5872, 0.4258)
11: (-0.5245, -0.2641, 0.5872, -0.4258)
12: (-0.2243, 0.7003, 0.7354, 0.2993)
13: (-0.2243, -0.7003, 0.7354, -0.2993)
14: (-0.3287, 0.5380, 0.6305, 0.3373)
15: (-0.3287, -0.5380, 0.6305, -0.3373)
16: ( 0.3527, 0.8513, 0.9215, 0.1875)
17: ( 0.3527, -0.8513, 0.9215, -0.1875)
18: (-0.0961, 0.5961, 0.6038, 0.2754)
19: (-0.0961, -0.5961, 0.6038, -0.2754)
20: ( 0.2624, 0.7219, 0.7681, 0.1945)
21: ( 0.2624, -0.7219, 0.7681, -0.1945)
22: ( 0.2109, 0.6545, 0.6876, 0.2004)
23: ( 0.2109, -0.6545, 0.6876, -0.2004)
24: (-0.2329, 0.0000, 0.2329, 0.5000)
25: (-0.1000, 0.0000, 0.1000, 0.5000)
26: ( 0.6966, 0.6594, 0.9592, 0.1206)
27: ( 0.6966, -0.6594, 0.9592, -0.1206)
28: ( 0.4453, 0.5594, 0.7149, 0.1430)
29: ( 0.4453, -0.5594, 0.7149, -0.1430)
30: ( 0.7258, 0.4395, 0.8485, 0.0866)
31: ( 0.7258, -0.4395, 0.8485, -0.0866)
32: ( 0.8118, 0.3423, 0.8810, 0.0635)
33: ( 0.8118, -0.3423, 0.8810, -0.0635)
34: ( 0.9206, 0.2748, 0.9608, 0.0462)
35: ( 0.9206, -0.2748, 0.9608, -0.0462)
36: ( 0.9928, 0.0788, 0.9959, 0.0126)
37: ( 0.9928, -0.0788, 0.9959, -0.0126)
38: ( 0.9958, 0.0000, 0.9958, 0.0000)
39: ( 0.8962, 0.1124, 0.9032, 0.0198)
40: ( 0.8962, -0.1124, 0.9032, -0.0198)
41: ( 0.5908, 0.2922, 0.6591, 0.0731)
42: ( 0.5908, -0.2922, 0.6591, -0.0731)
43: ( 0.5367, 0.2025, 0.5736, 0.0574)
44: ( 0.5367, -0.2025, 0.5736, -0.0574)
Hope that helps.
Cheers,
Mj
On Tue, Dec 13, 2011 at 12:51 PM, Summers, Peter <psummers(a)highpoint.edu>wrote:
I'm confused too.
MJ, is the (log) level of GDP one of the 11 series in your VAR? If so,
then based on the unit root tests you showed earlier, it is not "stable
(and stationary) without a trend." On the contrary, it has a unit root --
and is therefore non-stationary -- whether or not a deterministic trend is
included in the dgp.
In other words, including the level of GDP in your reduced-form VAR
renders it non-stationary.
Back to the potential small-sample issue: a VAR with 11 variables and 4
lags has 44 parameters per equation, not counting a constant (or trend?!).
There are also 55 parameters in the covariance matrix. With 100
observations per series, you're asking quite a lot of your data set. Even
if you knew the covariance matrix for sure, you'd have just over 2
obs/parameter for estimating the dynamics. I don't think that's asymptotic
yet, but I could be wrong ;-)
________________________________
From: gretl-users-bounces(a)lists.wfu.edu [gretl-users-bounces(a)lists.wfu.edu]
on behalf of Dr RJF Hudson [rjfhud(a)powerup.com.au]
Sent: Monday, December 12, 2011 8:28 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Greetings all
Have to say I'm getting confused, here.
I'd be appreciative please if somebody would tell me please
what this means "the reduced form".... of what?
Also if a set is stable as you say, and to produce its stationarity you
are confident that you haven't
squelched out important information from the data by differencing etc,
what's the reason to introduce trend information and then trust inferences
from the results ?
Trend in their Unit Roots?
I'm cool
rest easy
Richard Hudson
Dr RJF Hudson Qld Australia
rjfhud@powerup.com.au<mailto:rjfhud@powerup.com.au>
----- Original Message -----
From: Muheed Jamaldeen<mailto:mj.myworld@gmail.com>
To: Gretl list<mailto:gretl-users@lists.wfu.edu>
Sent: Tuesday, December 13, 2011 10:59 AM
Subject: Re: [Gretl-users] Deterministic trend in VAR
You're right about the VAR not being stable if USGDP were the only series
in the model. Well, the VAR is a 11 variable VAR (4). The 11 variables are
GDP and macroeconomic variables.
I am testing the impact of cash rate innovations on GDP. The question is,
if the reduced form is stable (and stationary) WITHOUT a trend, should one
include a trend when the univariate tests suggest that SOME of the series
may have trend in their unit roots.
Hope that makes sense?
On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter <psummers(a)highpoint.edu
<mailto:psummers@highpoint.edu>> wrote:
MJ,
You're right that the unit root tests are telling you that you have a unit
root in at least one series.
I'm confused about what your VAR looks like though (and maybe the rest of
the list is too). If this is one of the series in your VAR, then it's not
stable/stationary, by definition. That is, the lag operator polynomial will
have at least one root on the unit circle. My earlier answer assumed that
your unit root & cointegration tests ruled out both, but now it seems
that's not the case.
Relating to ths, how many series do you have in your VAR? My feeling is
that 100 obs per series isn't really a lot, especially if you're trying to
sort out issues related to deterministic vs stochastic trends,
cointegration vs none, etc.
At this point I'd suggest a) reading the gretl manual and/or your favorite
reference on VARs & VECMs, and/or b) providing some more detail about what
you're trying to do.
PS
________________________________
From: gretl-users-bounces(a)lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu> [gretl-users-bounces(a)lists.wfu.edu
<mailto:gretl-users-bounces@lists.wfu.edu>] on behalf of Muheed Jamaldeen
[mj.myworld@gmail.com<mailto:mj.myworld@gmail.com>]
Sent: Monday, December 12, 2011 6:59 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Peter,
I have 100 observations in the model. So small samples may or may not be
an issue. I am wondering if the deterministic trend is an issue at all
because the VAR is stable implying stationarity of the described process in
each equation WITHOUT the trend (i.e. the polynomial defined by the
determinant of the autoregressive operator has no roots in and on the
complex unit circle without the time trend term).
The ADF tests suggest that we cannot reject the trend term. Let me show
you an example. Following is the ADF tests for logged US GDP.
Monte Carlo studies suggest that choosing the lag order (p) of the unit
root tests according to the formula: Int {12(T /100)1/ 4} so the lag order
is 12 with 100 observations.
test without constant
test statistic: tau_nc(1) = 2.13551
asymptotic p-value 0.9927
test with constant
test statistic: tau_c(1) = -1.28148
asymptotic p-value 0.6405
with constant and trend
test statistic: tau_ct(1) = -0.728436
asymptotic p-value 0.9702
Following is the estimate for the trend term in the last ADF regression.
coefficient std. error t-ratio p-value
-------------------------------------------------------------
time 0.000200838 0.000317669 0.6322 0.5292
So all three tests are saying that I cannot reject the null of unit root.
Including I(1) variables in an unrestricted VAR is fine as Lutekepohl and
Toda and Yammoto have demonstrated. It's a question of whether a trend term
is to be included. I am inclined to think not because the VAR is stable
WITHOUT a trend.
Thoughts?
Cheers,
Mj
On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter <psummers(a)highpoint.edu
<mailto:psummers@highpoint.edu><mailto:psummers@highpoint.edu<mailto:
psummers(a)highpoint.edu>>> wrote:
MJ,
If your data have deterministic trends, then unit root tests should pick
that up (though there may be a problem in small samples). If you include a
trend but the dgp is stationary, then a t-test should conclude that the
trend coefficient is zero. Presumably your unit root tests reject the null,
right?
From: gretl-users-bounces(a)lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu><mailto:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>>
[mailto:gretl-users-bounces@lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu><mailto:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>>]
On Behalf Of Muheed Jamaldeen
Sent: Monday, December 12, 2011 5:52 AM
To: Gretl list
Subject: [Gretl-users] Deterministic trend in VAR
Hi all,
Just a general VAR related question. When is it appropriate to include a
deterministic time trend in the reduced form VAR? Visually some of the data
series (not all) look like they have trending properties. In any case, does
the inclusion of the time trend matter if the process is stable and
therefore stationary (i.e. the polynomial defined by the determinant of the
autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better
way to test whether the underlying data generating process has a stochastic
or deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu><mailto:
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>>
http://lists.wfu.edu/mailman/listinfo/gretl-users
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
http://lists.wfu.edu/mailman/listinfo/gretl-users
________________________________
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
2:41 a.m.
PS: JMULTI computes eigenvalues of the reverse characteristic polynomial
which must be greater than one for stability, while Gretl computes inverse
roots which must be less than 1.
On Tue, Dec 13, 2011 at 1:33 PM, Muheed Jamaldeen <mj.myworld(a)gmail.com>wrote:
Hi Peter,
Yes. USGDP is part of the 11 variables. I didn't want to clutter the list
with the rest of the tests and other information.
I am estimating the reduced form (near) VAR and SVAR on JMULTI whilst
using Gretl for preliminary testing. JMULTI computes modulus of the
eigenvalues of the reverse characteristic polynomial which are all greater
than one (which is the stability condition, implying stationarity).
Let me explain what I mean by stability implying stationarity using
Lutekepohl's text:
" The process is stable if det(IK − A1z − ·· ·− Apz p) = 0 for |z| ≤ 1,
(3.2) that is, the polynomial defined by the determinant of the
autoregressive operator has no roots in and on the complex unit circle. On
the assumption that the process has been initiated in the infinite past (t
= 0,±1,±2, . . .), it generates stationary time series that have
time-invariant means, variances, and covariance structure."
He makes a similar argument here:
http://books.google.com.au/books?id=muorJ6FHIiEC&q=Stable#v=snippet&a...
See the proposition in page 25.
That makes sense to me because regardless of what the univariate Data
Generating Process (DGP) suggests, the description of the process by each
VAR equation is stable, implying stationarity. If this is WITHOUT a trend
term, then is there a case for a trend term? That is the crux of the
question. The distinction is that the DGP may not be stationary, but the
VAR process is. So there is no problem if the VAR process is stable (and
thereby stationary) without a trend term.
I agree with your small sample point. But my hands are tied there! lol.
Also, for consistency I computed the VAR inverse roots on Gretl. They are
all inside the unit circle. Implying stability of the VAR process.
roots (real, imaginary, modulus, frequency)
1: (-0.6179, 0.4963, 0.7925, 0.3923)
2: (-0.6179, -0.4963, 0.7925, -0.3923)
3: (-0.7550, 0.0000, 0.7550, 0.5000)
4: (-0.7032, 0.1521, 0.7195, 0.4661)
5: (-0.7032, -0.1521, 0.7195, -0.4661)
6: (-0.4947, 0.6105, 0.7857, 0.3584)
7: (-0.4947, -0.6105, 0.7857, -0.3584)
8: (-0.5062, 0.3974, 0.6435, 0.3941)
9: (-0.5062, -0.3974, 0.6435, -0.3941)
10: (-0.5245, 0.2641, 0.5872, 0.4258)
11: (-0.5245, -0.2641, 0.5872, -0.4258)
12: (-0.2243, 0.7003, 0.7354, 0.2993)
13: (-0.2243, -0.7003, 0.7354, -0.2993)
14: (-0.3287, 0.5380, 0.6305, 0.3373)
15: (-0.3287, -0.5380, 0.6305, -0.3373)
16: ( 0.3527, 0.8513, 0.9215, 0.1875)
17: ( 0.3527, -0.8513, 0.9215, -0.1875)
18: (-0.0961, 0.5961, 0.6038, 0.2754)
19: (-0.0961, -0.5961, 0.6038, -0.2754)
20: ( 0.2624, 0.7219, 0.7681, 0.1945)
21: ( 0.2624, -0.7219, 0.7681, -0.1945)
22: ( 0.2109, 0.6545, 0.6876, 0.2004)
23: ( 0.2109, -0.6545, 0.6876, -0.2004)
24: (-0.2329, 0.0000, 0.2329, 0.5000)
25: (-0.1000, 0.0000, 0.1000, 0.5000)
26: ( 0.6966, 0.6594, 0.9592, 0.1206)
27: ( 0.6966, -0.6594, 0.9592, -0.1206)
28: ( 0.4453, 0.5594, 0.7149, 0.1430)
29: ( 0.4453, -0.5594, 0.7149, -0.1430)
30: ( 0.7258, 0.4395, 0.8485, 0.0866)
31: ( 0.7258, -0.4395, 0.8485, -0.0866)
32: ( 0.8118, 0.3423, 0.8810, 0.0635)
33: ( 0.8118, -0.3423, 0.8810, -0.0635)
34: ( 0.9206, 0.2748, 0.9608, 0.0462)
35: ( 0.9206, -0.2748, 0.9608, -0.0462)
36: ( 0.9928, 0.0788, 0.9959, 0.0126)
37: ( 0.9928, -0.0788, 0.9959, -0.0126)
38: ( 0.9958, 0.0000, 0.9958, 0.0000)
39: ( 0.8962, 0.1124, 0.9032, 0.0198)
40: ( 0.8962, -0.1124, 0.9032, -0.0198)
41: ( 0.5908, 0.2922, 0.6591, 0.0731)
42: ( 0.5908, -0.2922, 0.6591, -0.0731)
43: ( 0.5367, 0.2025, 0.5736, 0.0574)
44: ( 0.5367, -0.2025, 0.5736, -0.0574)
Hope that helps.
Cheers,
Mj
On Tue, Dec 13, 2011 at 12:51 PM, Summers, Peter <psummers(a)highpoint.edu>wrote:
> I'm confused too.
>
> MJ, is the (log) level of GDP one of the 11 series in your VAR? If so,
> then based on the unit root tests you showed earlier, it is not "stable
> (and stationary) without a trend." On the contrary, it has a unit root --
> and is therefore non-stationary -- whether or not a deterministic trend is
> included in the dgp.
>
> In other words, including the level of GDP in your reduced-form VAR
> renders it non-stationary.
>
> Back to the potential small-sample issue: a VAR with 11 variables and 4
> lags has 44 parameters per equation, not counting a constant (or trend?!).
> There are also 55 parameters in the covariance matrix. With 100
> observations per series, you're asking quite a lot of your data set. Even
> if you knew the covariance matrix for sure, you'd have just over 2
> obs/parameter for estimating the dynamics. I don't think that's asymptotic
> yet, but I could be wrong ;-)
>
>
> ________________________________
> From: gretl-users-bounces(a)lists.wfu.edu [
> gretl-users-bounces(a)lists.wfu.edu] on behalf of Dr RJF Hudson [
> rjfhud(a)powerup.com.au]
> Sent: Monday, December 12, 2011 8:28 PM
> To: Gretl list
> Subject: Re: [Gretl-users] Deterministic trend in VAR
>
> Greetings all
> Have to say I'm getting confused, here.
> I'd be appreciative please if somebody would tell me please
> what this means "the reduced form".... of what?
> Also if a set is stable as you say, and to produce its stationarity you
> are confident that you haven't
> squelched out important information from the data by differencing etc,
> what's the reason to introduce trend information and then trust inferences
> from the results ?
> Trend in their Unit Roots?
> I'm cool
> rest easy
> Richard Hudson
>
> Dr RJF Hudson Qld Australia
> rjfhud@powerup.com.au<mailto:rjfhud@powerup.com.au>
> ----- Original Message -----
> From: Muheed Jamaldeen<mailto:mj.myworld@gmail.com>
> To: Gretl list<mailto:gretl-users@lists.wfu.edu>
> Sent: Tuesday, December 13, 2011 10:59 AM
> Subject: Re: [Gretl-users] Deterministic trend in VAR
>
> You're right about the VAR not being stable if USGDP were the only series
> in the model. Well, the VAR is a 11 variable VAR (4). The 11 variables are
> GDP and macroeconomic variables.
>
> I am testing the impact of cash rate innovations on GDP. The question is,
> if the reduced form is stable (and stationary) WITHOUT a trend, should one
> include a trend when the univariate tests suggest that SOME of the series
> may have trend in their unit roots.
>
> Hope that makes sense?
>
>
> On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter <psummers(a)highpoint.edu
> <mailto:psummers@highpoint.edu>> wrote:
> MJ,
>
> You're right that the unit root tests are telling you that you have a
> unit root in at least one series.
>
> I'm confused about what your VAR looks like though (and maybe the rest of
> the list is too). If this is one of the series in your VAR, then it's not
> stable/stationary, by definition. That is, the lag operator polynomial will
> have at least one root on the unit circle. My earlier answer assumed that
> your unit root & cointegration tests ruled out both, but now it seems
> that's not the case.
>
> Relating to ths, how many series do you have in your VAR? My feeling is
> that 100 obs per series isn't really a lot, especially if you're trying to
> sort out issues related to deterministic vs stochastic trends,
> cointegration vs none, etc.
>
> At this point I'd suggest a) reading the gretl manual and/or your
> favorite reference on VARs & VECMs, and/or b) providing some more detail
> about what you're trying to do.
>
> PS
> ________________________________
> From: gretl-users-bounces(a)lists.wfu.edu<mailto:
> gretl-users-bounces(a)lists.wfu.edu> [gretl-users-bounces(a)lists.wfu.edu
> <mailto:gretl-users-bounces@lists.wfu.edu>] on behalf of Muheed
> Jamaldeen [mj.myworld@gmail.com<mailto:mj.myworld@gmail.com>]
> Sent: Monday, December 12, 2011 6:59 PM
> To: Gretl list
> Subject: Re: [Gretl-users] Deterministic trend in VAR
>
> Peter,
>
> I have 100 observations in the model. So small samples may or may not be
> an issue. I am wondering if the deterministic trend is an issue at all
> because the VAR is stable implying stationarity of the described process in
> each equation WITHOUT the trend (i.e. the polynomial defined by the
> determinant of the autoregressive operator has no roots in and on the
> complex unit circle without the time trend term).
>
> The ADF tests suggest that we cannot reject the trend term. Let me show
> you an example. Following is the ADF tests for logged US GDP.
>
> Monte Carlo studies suggest that choosing the lag order (p) of the unit
> root tests according to the formula: Int {12(T /100)1/ 4} so the lag order
> is 12 with 100 observations.
>
> test without constant
> test statistic: tau_nc(1) = 2.13551
> asymptotic p-value 0.9927
>
> test with constant
> test statistic: tau_c(1) = -1.28148
> asymptotic p-value 0.6405
>
> with constant and trend
> test statistic: tau_ct(1) = -0.728436
> asymptotic p-value 0.9702
>
> Following is the estimate for the trend term in the last ADF regression.
>
> coefficient std. error t-ratio p-value
> -------------------------------------------------------------
> time 0.000200838 0.000317669 0.6322 0.5292
>
> So all three tests are saying that I cannot reject the null of unit root.
> Including I(1) variables in an unrestricted VAR is fine as Lutekepohl and
> Toda and Yammoto have demonstrated. It's a question of whether a trend term
> is to be included. I am inclined to think not because the VAR is stable
> WITHOUT a trend.
>
> Thoughts?
>
> Cheers,
>
> Mj
>
> On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter <psummers(a)highpoint.edu
> <mailto:psummers@highpoint.edu><mailto:psummers@highpoint.edu<mailto:
> psummers(a)highpoint.edu>>> wrote:
> MJ,
>
> If your data have deterministic trends, then unit root tests should pick
> that up (though there may be a problem in small samples). If you include a
> trend but the dgp is stationary, then a t-test should conclude that the
> trend coefficient is zero. Presumably your unit root tests reject the null,
> right?
>
> From: gretl-users-bounces(a)lists.wfu.edu<mailto:
> gretl-users-bounces(a)lists.wfu.edu><mailto:
> gretl-users-bounces(a)lists.wfu.edu<mailto:
> gretl-users-bounces(a)lists.wfu.edu>> [mailto:
> gretl-users-bounces(a)lists.wfu.edu<mailto:
> gretl-users-bounces(a)lists.wfu.edu><mailto:
> gretl-users-bounces(a)lists.wfu.edu<mailto:
> gretl-users-bounces(a)lists.wfu.edu>>] On Behalf Of Muheed Jamaldeen
> Sent: Monday, December 12, 2011 5:52 AM
> To: Gretl list
> Subject: [Gretl-users] Deterministic trend in VAR
>
> Hi all,
> Just a general VAR related question. When is it appropriate to include a
> deterministic time trend in the reduced form VAR? Visually some of the data
> series (not all) look like they have trending properties. In any case, does
> the inclusion of the time trend matter if the process is stable and
> therefore stationary (i.e. the polynomial defined by the determinant of the
> autoregressive operator has no roots in and on the complex unit circle)
> without the time trend term. Other than unit root tests, is there a better
> way to test whether the underlying data generating process has a stochastic
> or deterministic process?
>
> I am mainly interested in the impulse responses.
>
> Cheers,
>
> Mj
>
>
> _______________________________________________
> Gretl-users mailing list
> Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu><mailto:
> Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>>
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
>
> _______________________________________________
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> Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
>
> ________________________________
>
> _______________________________________________
> Gretl-users mailing list
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>
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> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
9:20 a.m.
Hi everybody
'scuse my sixpennyworth cos I'm still confused and don't really want to
get involved but I'm thinking that always that unit roots need to be outside the unit
circle.
The question here is, Are they ?.
Stationarity about a trendline means there is information in the data not yet described.
If the trend information is removed then any inferences that follow are not about the
original data.
Gretl can handle all of this I'd be certain.
Long before Gretl when I was researching,there was a lack of great proggies such as
Gretl.
This compelled me to write my own programs. I'm thinking that researchers who
haven't learned
Wayne Fuller's and David Dickey's stuff off by heart from Fuller's book or
their joint work,
coupled with Solo, Evans & Savin,Banajee and Hendry, Said and Dickey, etc etc might
like to give
them a good read. I'm merely minding that its tough to be valid with Unit root stuff.
Hudson
Dr RJF Hudson Qld Australia
rjfhud(a)powerup.com.au
----- Original Message -----
From: Muheed Jamaldeen
To: Gretl list
Sent: Tuesday, December 13, 2011 12:41 PM
Subject: Re: [Gretl-users] Deterministic trend in VAR
PS: JMULTI computes eigenvalues of the reverse characteristic polynomial which must be
greater than one for stability, while Gretl computes inverse roots which must be less than
1.
On Tue, Dec 13, 2011 at 1:33 PM, Muheed Jamaldeen <mj.myworld(a)gmail.com> wrote:
Hi Peter,
Yes. USGDP is part of the 11 variables. I didn't want to clutter the list with the
rest of the tests and other information.
I am estimating the reduced form (near) VAR and SVAR on JMULTI whilst using Gretl for
preliminary testing. JMULTI computes modulus of the eigenvalues of the reverse
characteristic polynomial which are all greater than one (which is the stability
condition, implying stationarity).
Let me explain what I mean by stability implying stationarity using Lutekepohl's
text:
" The process is stable if det(IK − A1z − ·· ·− Apz p) = 0 for |z| ≤ 1, (3.2)
that is, the polynomial defined by the determinant of the autoregressive operator has no
roots in and on the complex unit circle. On the assumption that the process has been
initiated in the infinite past (t = 0,±1,±2, . . .), it generates stationary time series
that have time-invariant means, variances, and covariance structure."
He makes a similar argument here:
http://books.google.com.au/books?id=muorJ6FHIiEC&q=Stable#v=snippet&a...
See the proposition in page 25.
That makes sense to me because regardless of what the univariate Data Generating
Process (DGP) suggests, the description of the process by each VAR equation is stable,
implying stationarity. If this is WITHOUT a trend term, then is there a case for a trend
term? That is the crux of the question. The distinction is that the DGP may not be
stationary, but the VAR process is. So there is no problem if the VAR process is stable
(and thereby stationary) without a trend term.
I agree with your small sample point. But my hands are tied there! lol.
Also, for consistency I computed the VAR inverse roots on Gretl. They are all inside
the unit circle. Implying stability of the VAR process.
roots (real, imaginary, modulus, frequency)
1: (-0.6179, 0.4963, 0.7925, 0.3923)
2: (-0.6179, -0.4963, 0.7925, -0.3923)
3: (-0.7550, 0.0000, 0.7550, 0.5000)
4: (-0.7032, 0.1521, 0.7195, 0.4661)
5: (-0.7032, -0.1521, 0.7195, -0.4661)
6: (-0.4947, 0.6105, 0.7857, 0.3584)
7: (-0.4947, -0.6105, 0.7857, -0.3584)
8: (-0.5062, 0.3974, 0.6435, 0.3941)
9: (-0.5062, -0.3974, 0.6435, -0.3941)
10: (-0.5245, 0.2641, 0.5872, 0.4258)
11: (-0.5245, -0.2641, 0.5872, -0.4258)
12: (-0.2243, 0.7003, 0.7354, 0.2993)
13: (-0.2243, -0.7003, 0.7354, -0.2993)
14: (-0.3287, 0.5380, 0.6305, 0.3373)
15: (-0.3287, -0.5380, 0.6305, -0.3373)
16: ( 0.3527, 0.8513, 0.9215, 0.1875)
17: ( 0.3527, -0.8513, 0.9215, -0.1875)
18: (-0.0961, 0.5961, 0.6038, 0.2754)
19: (-0.0961, -0.5961, 0.6038, -0.2754)
20: ( 0.2624, 0.7219, 0.7681, 0.1945)
21: ( 0.2624, -0.7219, 0.7681, -0.1945)
22: ( 0.2109, 0.6545, 0.6876, 0.2004)
23: ( 0.2109, -0.6545, 0.6876, -0.2004)
24: (-0.2329, 0.0000, 0.2329, 0.5000)
25: (-0.1000, 0.0000, 0.1000, 0.5000)
26: ( 0.6966, 0.6594, 0.9592, 0.1206)
27: ( 0.6966, -0.6594, 0.9592, -0.1206)
28: ( 0.4453, 0.5594, 0.7149, 0.1430)
29: ( 0.4453, -0.5594, 0.7149, -0.1430)
30: ( 0.7258, 0.4395, 0.8485, 0.0866)
31: ( 0.7258, -0.4395, 0.8485, -0.0866)
32: ( 0.8118, 0.3423, 0.8810, 0.0635)
33: ( 0.8118, -0.3423, 0.8810, -0.0635)
34: ( 0.9206, 0.2748, 0.9608, 0.0462)
35: ( 0.9206, -0.2748, 0.9608, -0.0462)
36: ( 0.9928, 0.0788, 0.9959, 0.0126)
37: ( 0.9928, -0.0788, 0.9959, -0.0126)
38: ( 0.9958, 0.0000, 0.9958, 0.0000)
39: ( 0.8962, 0.1124, 0.9032, 0.0198)
40: ( 0.8962, -0.1124, 0.9032, -0.0198)
41: ( 0.5908, 0.2922, 0.6591, 0.0731)
42: ( 0.5908, -0.2922, 0.6591, -0.0731)
43: ( 0.5367, 0.2025, 0.5736, 0.0574)
44: ( 0.5367, -0.2025, 0.5736, -0.0574)
Hope that helps.
Cheers,
Mj
On Tue, Dec 13, 2011 at 12:51 PM, Summers, Peter <psummers(a)highpoint.edu>
wrote:
I'm confused too.
MJ, is the (log) level of GDP one of the 11 series in your VAR? If so, then based on
the unit root tests you showed earlier, it is not "stable (and stationary) without a
trend." On the contrary, it has a unit root -- and is therefore non-stationary --
whether or not a deterministic trend is included in the dgp.
In other words, including the level of GDP in your reduced-form VAR renders it
non-stationary.
Back to the potential small-sample issue: a VAR with 11 variables and 4 lags has 44
parameters per equation, not counting a constant (or trend?!). There are also 55
parameters in the covariance matrix. With 100 observations per series, you're asking
quite a lot of your data set. Even if you knew the covariance matrix for sure, you'd
have just over 2 obs/parameter for estimating the dynamics. I don't think that's
asymptotic yet, but I could be wrong ;-)
________________________________
From: gretl-users-bounces(a)lists.wfu.edu [gretl-users-bounces(a)lists.wfu.edu] on
behalf of Dr RJF Hudson [rjfhud(a)powerup.com.au]
Sent: Monday, December 12, 2011 8:28 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Greetings all
Have to say I'm getting confused, here.
I'd be appreciative please if somebody would tell me please
what this means "the reduced form".... of what?
Also if a set is stable as you say, and to produce its stationarity you are
confident that you haven't
squelched out important information from the data by differencing etc, what's
the reason to introduce trend information and then trust inferences from the results ?
Trend in their Unit Roots?
I'm cool
rest easy
Richard Hudson
Dr RJF Hudson Qld Australia
rjfhud@powerup.com.au<mailto:rjfhud@powerup.com.au>
----- Original Message -----
From: Muheed Jamaldeen<mailto:mj.myworld@gmail.com>
To: Gretl list<mailto:gretl-users@lists.wfu.edu>
Sent: Tuesday, December 13, 2011 10:59 AM
Subject: Re: [Gretl-users] Deterministic trend in VAR
You're right about the VAR not being stable if USGDP were the only series in the
model. Well, the VAR is a 11 variable VAR (4). The 11 variables are GDP and macroeconomic
variables.
I am testing the impact of cash rate innovations on GDP. The question is, if the
reduced form is stable (and stationary) WITHOUT a trend, should one include a trend when
the univariate tests suggest that SOME of the series may have trend in their unit roots.
Hope that makes sense?
On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter
<psummers@highpoint.edu<mailto:psummers@highpoint.edu>> wrote:
MJ,
You're right that the unit root tests are telling you that you have a unit root
in at least one series.
I'm confused about what your VAR looks like though (and maybe the rest of the
list is too). If this is one of the series in your VAR, then it's not
stable/stationary, by definition. That is, the lag operator polynomial will have at least
one root on the unit circle. My earlier answer assumed that your unit root &
cointegration tests ruled out both, but now it seems that's not the case.
Relating to ths, how many series do you have in your VAR? My feeling is that 100 obs
per series isn't really a lot, especially if you're trying to sort out issues
related to deterministic vs stochastic trends, cointegration vs none, etc.
At this point I'd suggest a) reading the gretl manual and/or your favorite
reference on VARs & VECMs, and/or b) providing some more detail about what you're
trying to do.
PS
________________________________
From:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>
[gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>] on
behalf of Muheed Jamaldeen [mj.myworld@gmail.com<mailto:mj.myworld@gmail.com>]
Sent: Monday, December 12, 2011 6:59 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Peter,
I have 100 observations in the model. So small samples may or may not be an issue. I
am wondering if the deterministic trend is an issue at all because the VAR is stable
implying stationarity of the described process in each equation WITHOUT the trend (i.e.
the polynomial defined by the determinant of the autoregressive operator has no roots in
and on the complex unit circle without the time trend term).
The ADF tests suggest that we cannot reject the trend term. Let me show you an
example. Following is the ADF tests for logged US GDP.
Monte Carlo studies suggest that choosing the lag order (p) of the unit root tests
according to the formula: Int {12(T /100)1/ 4} so the lag order is 12 with 100
observations.
test without constant
test statistic: tau_nc(1) = 2.13551
asymptotic p-value 0.9927
test with constant
test statistic: tau_c(1) = -1.28148
asymptotic p-value 0.6405
with constant and trend
test statistic: tau_ct(1) = -0.728436
asymptotic p-value 0.9702
Following is the estimate for the trend term in the last ADF regression.
coefficient std. error t-ratio p-value
-------------------------------------------------------------
time 0.000200838 0.000317669 0.6322 0.5292
So all three tests are saying that I cannot reject the null of unit root. Including
I(1) variables in an unrestricted VAR is fine as Lutekepohl and Toda and Yammoto have
demonstrated. It's a question of whether a trend term is to be included. I am inclined
to think not because the VAR is stable WITHOUT a trend.
Thoughts?
Cheers,
Mj
On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter
<psummers@highpoint.edu<mailto:psummers@highpoint.edu><mailto:psummers@highpoint.edu<mailto:psummers@highpoint.edu>>>
wrote:
MJ,
If your data have deterministic trends, then unit root tests should pick that up
(though there may be a problem in small samples). If you include a trend but the dgp is
stationary, then a t-test should conclude that the trend coefficient is zero. Presumably
your unit root tests reject the null, right?
From:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu><mailto:gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>>
[mailto:gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu><mailto:gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>>]
On Behalf Of Muheed Jamaldeen
Sent: Monday, December 12, 2011 5:52 AM
To: Gretl list
Subject: [Gretl-users] Deterministic trend in VAR
Hi all,
Just a general VAR related question. When is it appropriate to include a
deterministic time trend in the reduced form VAR? Visually some of the data series (not
all) look like they have trending properties. In any case, does the inclusion of the time
trend matter if the process is stable and therefore stationary (i.e. the polynomial
defined by the determinant of the autoregressive operator has no roots in and on the
complex unit circle) without the time trend term. Other than unit root tests, is there a
better way to test whether the underlying data generating process has a stochastic or
deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
_______________________________________________
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7:06 a.m.
On Tue, 13 Dec 2011, Muheed Jamaldeen wrote:
JMULTI computes modulus of the eigenvalues
of the reverse characteristic polynomial which are all greater than one
(which is the stability condition, implying stationarity).
[...]
Also, for consistency I computed the VAR inverse roots on Gretl. They
are
all inside the unit circle. Implying stability of the VAR process.
You cannot decide on the number of unit roots in a VAR simply by looking
at the estimated eigenvalues (unless you happen to have magical powers,
but in that case you don't need econometrics at all). This is because the
properties you cite hold for the TRUE eigenvalues (whatever that means),
but you only see their estimates, which are different with probability 1.
In most cases, estimated eigenvalues do converge in probability to the
true ones, because of consistency of the VAR estimated coefficients and
the fact that eigenvalues are a continuous function of the companion
matrix, so you can invoke the continuous mapping theorem, but their
asymptotic distribution is decidedly weird. I remember reading a paper a
few years ago about the fact that if you estimate a VAR(p) over white
noise data, the aymptotic properties of the estimated eigenvaules are
such that, as p grows, you're bound to find them uniformly scattered
AROUND THE UNIT CIRCLE. Actually, I can't find the paper right now, so I'd
be grateful if anybody could give me a pointer (and yes, I've already
googled for it).
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
6:42 a.m.
On Tue, 13 Dec 2011, Summers, Peter wrote:
Back to the potential small-sample issue: a VAR with 11 variables and
4
lags has 44 parameters per equation, not counting a constant (or
trend?!). There are also 55 parameters in the covariance matrix. With
100 observations per series, you're asking quite a lot of your data set.
Even if you knew the covariance matrix for sure, you'd have just over 2
obs/parameter for estimating the dynamics. I don't think that's
asymptotic yet, but I could be wrong ;-)
Amen, brother!
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti
10:11 a.m.
One should not even think of estimating an 11 variable VAR(4) with 100
observations. Standard errors will be so large that any null will be
acceptable an tests will have no power. If he draws impulse response
functions confidence intervals will be so large that he will be unable to
draw any conclusions. Is there no way that the number of variables can be
reduced to say 3-5
On Tuesday, 13 December 2011, Summers, Peter <psummers(a)highpoint.edu> wrote:
I'm confused too.
MJ, is the (log) level of GDP one of the 11 series in your VAR? If so,
then based
on the unit root tests you showed earlier, it is not "stable
(and stationary) without a trend." On the contrary, it has a unit root --
and is therefore non-stationary -- whether or not a deterministic trend is
included in the dgp.
In other words, including the level of GDP in your reduced-form VAR
renders it
non-stationary.
Back to the potential small-sample issue: a VAR with 11 variables and 4
lags has 44
parameters per equation, not counting a constant (or trend?!).
There are also 55 parameters in the covariance matrix. With 100
observations per series, you're asking quite a lot of your data set. Even
if you knew the covariance matrix for sure, you'd have just over 2
obs/parameter for estimating the dynamics. I don't think that's asymptotic
yet, but I could be wrong ;-)
________________________________
From: gretl-users-bounces(a)lists.wfu.edu [gretl-users-bounces(a)lists.wfu.edu]
on
behalf of Dr RJF Hudson [rjfhud(a)powerup.com.au]
Sent: Monday, December 12, 2011 8:28 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Greetings all
Have to say I'm getting confused, here.
I'd be appreciative please if somebody would tell me please
what this means "the reduced form".... of what?
Also if a set is stable as you say, and to produce its stationarity you
are
confident that you haven't
squelched out important information from the data by differencing
etc,
what's the reason to introduce trend information and then trust inferences
from the results ?
Trend in their Unit Roots?
I'm cool
rest easy
Richard Hudson
Dr RJF Hudson Qld Australia
rjfhud@powerup.com.au<mailto:rjfhud@powerup.com.au>
----- Original Message -----
From: Muheed Jamaldeen<mailto:mj.myworld@gmail.com>
To: Gretl list<mailto:gretl-users@lists.wfu.edu>
Sent: Tuesday, December 13, 2011 10:59 AM
Subject: Re: [Gretl-users] Deterministic trend in VAR
You're right about the VAR not being stable if USGDP were the only series
in
the model. Well, the VAR is a 11 variable VAR (4). The 11 variables are
GDP and macroeconomic variables.
I am testing the impact of cash rate innovations on GDP. The question is,
if the
reduced form is stable (and stationary) WITHOUT a trend, should one
include a trend when the univariate tests suggest that SOME of the series
may have trend in their unit roots.
Hope that makes sense?
On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter <psummers(a)highpoint.edu
<mailto:psummers@highpoint.edu>> wrote:
MJ,
You're right that the unit root tests are telling you that you have a
unit root
in at least one series.
I'm confused about what your VAR looks like though (and maybe the rest of
the
list is too). If this is one of the series in your VAR, then it's not
stable/stationary, by definition. That is, the lag operator polynomial will
have at least one root on the unit circle. My earlier answer assumed that
your unit root & cointegration tests ruled out both, but now it seems
that's not the case.
Relating to ths, how many series do you have in your VAR? My feeling is
that 100
obs per series isn't really a lot, especially if you're trying to
sort out issues related to deterministic vs stochastic trends,
cointegration vs none, etc.
At this point I'd suggest a) reading the gretl manual and/or your
favorite
reference on VARs & VECMs, and/or b) providing some more detail
about what you're trying to do.
PS
________________________________
From: gretl-users-bounces(a)lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu> [gretl-users-bounces(a)lists.wfu.edu
<mailto:gretl-users-bounces@lists.wfu.edu>] on behalf of Muheed Jamaldeen [
mj.myworld@gmail.com<mailto:mj.myworld@gmail.com>]
Sent: Monday, December 12, 2011 6:59 PM
To: Gretl list
Subject: Re: [Gretl-users] Deterministic trend in VAR
Peter,
I have 100 observations in the model. So small samples may or may not be
an issue.
I am wondering if the deterministic trend is an issue at all
because the VAR is stable implying stationarity of the described process in
each equation WITHOUT the trend (i.e. the polynomial defined by the
determinant of the autoregressive operator has no roots in and on the
complex unit circle without the time trend term).
The ADF tests suggest that we cannot reject the trend term. Let me show
you an
example. Following is the ADF tests for logged US GDP.
Monte Carlo studies suggest that choosing the lag order (p) of the unit
root tests
according to the formula: Int {12(T /100)1/ 4} so the lag order
is 12 with 100 observations.
test without constant
test statistic: tau_nc(1) = 2.13551
asymptotic p-value 0.9927
test with constant
test statistic: tau_c(1) = -1.28148
asymptotic p-value 0.6405
with constant and trend
test statistic: tau_ct(1) = -0.728436
asymptotic p-value 0.9702
Following is the estimate for the trend term in the last ADF regression.
coefficient std. error t-ratio p-value
-------------------------------------------------------------
time 0.000200838 0.000317669 0.6322 0.5292
So all three tests are saying that I cannot reject the null of unit root.
Including
I(1) variables in an unrestricted VAR is fine as Lutekepohl and
Toda and Yammoto have demonstrated. It's a question of whether a trend term
is to be included. I am inclined to think not because the VAR is stable
WITHOUT a trend.
Thoughts?
Cheers,
Mj
On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter <psummers(a)highpoint.edu
<mailto:psummers@highpoint.edu><mailto:psummers@highpoint.edu<mailto:
psummers(a)highpoint.edu>>> wrote:
MJ,
If your data have deterministic trends, then unit root tests should pick
that up
(though there may be a problem in small samples). If you include a
trend but the dgp is stationary, then a t-test should conclude that the
trend coefficient is zero. Presumably your unit root tests reject the null,
right?
From: gretl-users-bounces(a)lists.wfu.edu<mailto:
gretl-users-bounces@lists.wfu.edu><mailto:gretl-users-bounces@lists.wfu.edu
<mailto:gretl-users-bounces@lists.wfu.edu>> [mailto:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu
<mailto:gretl-users-bounces@lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu>>] On Behalf Of Muheed Jamaldeen
Sent: Monday, December 12, 2011 5:52 AM
To: Gretl list
Subject: [Gretl-users] Deterministic trend in VAR
Hi all,
Just a general VAR related question. When is it appropriate to include a
deterministic time trend in the reduced form VAR? Visually some of the data
series (not all) look like they have trending properties. In any case, does
the inclusion of the time trend matter if the process is stable and
therefore stationary (i.e. the polynomial defined by the determinant of the
autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better
way to test whether the underlying data generating process has a stochastic
or deterministic process?
I am mainly interested in the impulse responses.
Cheers,
Mj
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu><mailto:
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>>
http://lists.wfu.edu/mailman/listinfo/gretl-users
_______________________________________________
Gretl-users mailing list
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
http://lists.wfu.edu/mailman/listinfo/gretl-users
________________________________
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
12:10 a.m.
Thanks for all the helpful thoughts and comments everyone! : )
On Tue, Dec 13, 2011 at 9:11 PM, John C Frain <frainj(a)gmail.com> wrote:
One should not even think of estimating an 11 variable VAR(4) with
100
observations. Standard errors will be so large that any null will be
acceptable an tests will have no power. If he draws impulse response
functions confidence intervals will be so large that he will be unable to
draw any conclusions. Is there no way that the number of variables can be
reduced to say 3-5
On Tuesday, 13 December 2011, Summers, Peter <psummers(a)highpoint.edu>
wrote:
> I'm confused too.
>
> MJ, is the (log) level of GDP one of the 11 series in your VAR? If so,
then based on the unit root tests you showed earlier, it is not "stable
(and stationary) without a trend." On the contrary, it has a unit root --
and is therefore non-stationary -- whether or not a deterministic trend is
included in the dgp.
>
> In other words, including the level of GDP in your reduced-form VAR
renders it non-stationary.
>
> Back to the potential small-sample issue: a VAR with 11 variables and 4
lags has 44 parameters per equation, not counting a constant (or trend?!).
There are also 55 parameters in the covariance matrix. With 100
observations per series, you're asking quite a lot of your data set. Even
if you knew the covariance matrix for sure, you'd have just over 2
obs/parameter for estimating the dynamics. I don't think that's asymptotic
yet, but I could be wrong ;-)
>
>
> ________________________________
> From: gretl-users-bounces(a)lists.wfu.edu [
gretl-users-bounces(a)lists.wfu.edu] on behalf of Dr RJF Hudson [
rjfhud(a)powerup.com.au]
> Sent: Monday, December 12, 2011 8:28 PM
> To: Gretl list
> Subject: Re: [Gretl-users] Deterministic trend in VAR
>
> Greetings all
> Have to say I'm getting confused, here.
> I'd be appreciative please if somebody would tell me please
> what this means "the reduced form".... of what?
> Also if a set is stable as you say, and to produce its stationarity you
are confident that you haven't
> squelched out important information from the data by differencing etc,
what's the reason to introduce trend information and then trust inferences
from the results ?
> Trend in their Unit Roots?
> I'm cool
> rest easy
> Richard Hudson
>
> Dr RJF Hudson Qld Australia
> rjfhud@powerup.com.au<mailto:rjfhud@powerup.com.au>
> ----- Original Message -----
> From: Muheed Jamaldeen<mailto:mj.myworld@gmail.com>
> To: Gretl list<mailto:gretl-users@lists.wfu.edu>
> Sent: Tuesday, December 13, 2011 10:59 AM
> Subject: Re: [Gretl-users] Deterministic trend in VAR
>
> You're right about the VAR not being stable if USGDP were the only
series in the model. Well, the VAR is a 11 variable VAR (4). The 11
variables are GDP and macroeconomic variables.
>
> I am testing the impact of cash rate innovations on GDP. The question
is, if the reduced form is stable (and stationary) WITHOUT a trend, should
one include a trend when the univariate tests suggest that SOME of the
series may have trend in their unit roots.
>
> Hope that makes sense?
>
>
> On Tue, Dec 13, 2011 at 11:46 AM, Summers, Peter <psummers(a)highpoint.edu
<mailto:psummers@highpoint.edu>> wrote:
> MJ,
>
> You're right that the unit root tests are telling you that you have a
unit root in at least one series.
>
> I'm confused about what your VAR looks like though (and maybe the rest
of the list is too). If this is one of the series in your VAR, then it's
not stable/stationary, by definition. That is, the lag operator polynomial
will have at least one root on the unit circle. My earlier answer assumed
that your unit root & cointegration tests ruled out both, but now it seems
that's not the case.
>
> Relating to ths, how many series do you have in your VAR? My feeling is
that 100 obs per series isn't really a lot, especially if you're trying to
sort out issues related to deterministic vs stochastic trends,
cointegration vs none, etc.
>
> At this point I'd suggest a) reading the gretl manual and/or your
favorite reference on VARs & VECMs, and/or b) providing some more detail
about what you're trying to do.
>
> PS
> ________________________________
> From: gretl-users-bounces(a)lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu> [gretl-users-bounces(a)lists.wfu.edu
<mailto:gretl-users-bounces@lists.wfu.edu>] on behalf of Muheed Jamaldeen
[mj.myworld@gmail.com<mailto:mj.myworld@gmail.com>]
> Sent: Monday, December 12, 2011 6:59 PM
> To: Gretl list
> Subject: Re: [Gretl-users] Deterministic trend in VAR
>
> Peter,
>
> I have 100 observations in the model. So small samples may or may not be
an issue. I am wondering if the deterministic trend is an issue at all
because the VAR is stable implying stationarity of the described process in
each equation WITHOUT the trend (i.e. the polynomial defined by the
determinant of the autoregressive operator has no roots in and on the
complex unit circle without the time trend term).
>
> The ADF tests suggest that we cannot reject the trend term. Let me show
you an example. Following is the ADF tests for logged US GDP.
>
> Monte Carlo studies suggest that choosing the lag order (p) of the unit
root tests according to the formula: Int {12(T /100)1/ 4} so the lag order
is 12 with 100 observations.
>
> test without constant
> test statistic: tau_nc(1) = 2.13551
> asymptotic p-value 0.9927
>
> test with constant
> test statistic: tau_c(1) = -1.28148
> asymptotic p-value 0.6405
>
> with constant and trend
> test statistic: tau_ct(1) = -0.728436
> asymptotic p-value 0.9702
>
> Following is the estimate for the trend term in the last ADF regression.
>
> coefficient std. error t-ratio
p-value
> -------------------------------------------------------------
> time 0.000200838 0.000317669 0.6322 0.5292
>
> So all three tests are saying that I cannot reject the null of unit
root. Including I(1) variables in an unrestricted VAR is fine as Lutekepohl
and Toda and Yammoto have demonstrated. It's a question of whether a trend
term is to be included. I am inclined to think not because the VAR is
stable WITHOUT a trend.
>
> Thoughts?
>
> Cheers,
>
> Mj
>
> On Tue, Dec 13, 2011 at 1:17 AM, Summers, Peter <psummers(a)highpoint.edu
<mailto:psummers@highpoint.edu><mailto:psummers@highpoint.edu<mailto:
psummers(a)highpoint.edu>>> wrote:
> MJ,
>
> If your data have deterministic trends, then unit root tests should pick
that up (though there may be a problem in small samples). If you include a
trend but the dgp is stationary, then a t-test should conclude that the
trend coefficient is zero. Presumably your unit root tests reject the null,
right?
>
> From: gretl-users-bounces(a)lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu><mailto:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>>
[mailto:gretl-users-bounces@lists.wfu.edu<mailto:
gretl-users-bounces(a)lists.wfu.edu><mailto:
gretl-users-bounces@lists.wfu.edu<mailto:gretl-users-bounces@lists.wfu.edu>>]
On Behalf Of Muheed Jamaldeen
> Sent: Monday, December 12, 2011 5:52 AM
> To: Gretl list
> Subject: [Gretl-users] Deterministic trend in VAR
>
> Hi all,
> Just a general VAR related question. When is it appropriate to include a
deterministic time trend in the reduced form VAR? Visually some of the data
series (not all) look like they have trending properties. In any case, does
the inclusion of the time trend matter if the process is stable and
therefore stationary (i.e. the polynomial defined by the determinant of the
autoregressive operator has no roots in and on the complex unit circle)
without the time trend term. Other than unit root tests, is there a better
way to test whether the underlying data generating process has a stochastic
or deterministic process?
>
> I am mainly interested in the impulse responses.
>
> Cheers,
>
> Mj
>
>
> _______________________________________________
> Gretl-users mailing list
> Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu><mailto:
Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>>
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
>
> _______________________________________________
> Gretl-users mailing list
> Gretl-users@lists.wfu.edu<mailto:Gretl-users@lists.wfu.edu>
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
>
> ________________________________
>
> _______________________________________________
> Gretl-users mailing list
> Gretl-users(a)lists.wfu.edu
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
> _______________________________________________
> Gretl-users mailing list
> Gretl-users(a)lists.wfu.edu
> http://lists.wfu.edu/mailman/listinfo/gretl-users
>
_______________________________________________
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http://lists.wfu.edu/mailman/listinfo/gretl-users
10:51 a.m.
New subject: importing nominal variable
Dear All,
Something went wrong with my gretl 1.9.7, Windows. When importing
the ab.txt file
a b
1 b1
2 b1
3 b2
I get 0's for b. What I am doing wrong?
Thank you,
Rem
10:53 a.m.
New subject: importing nominal variable
On 02/09/2012 11:51 AM, Remigijus Lapinskas wrote:
Dear All,
Something went wrong with my gretl 1.9.7, Windows. When importing
the ab.txt file
a b
1 b1
2 b1
3 b2
I get 0's for b. What I am doing wrong?
Well you have non-numerical values for b -- what is that supposed to mean?
-sven
11:09 a.m.
New subject: importing nominal variable
Write, but it seems they used to be recoded to 1 1 2?
Rem
On 2012.02.09 12:53, Sven Schreiber wrote:
On 02/09/2012 11:51 AM, Remigijus Lapinskas wrote:
> Dear All,
>
> Something went wrong with my gretl 1.9.7, Windows. When importing
> the ab.txt file
>
> a b
> 1 b1
> 2 b1
> 3 b2
>
> I get 0's for b. What I am doing wrong?
>
Well you have non-numerical values for b -- what is that supposed to mean?
-sven
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
11:11 a.m.
New subject: importing nominal variable
Sorry, I ment
Right, but it seems they used to be recoded to 1 1 2?
Rem
On 2012.02.09 12:53, Sven Schreiber wrote:
On 02/09/2012 11:51 AM, Remigijus Lapinskas wrote:
> Dear All,
>
> Something went wrong with my gretl 1.9.7, Windows. When importing
> the ab.txt file
>
> a b
> 1 b1
> 2 b1
> 3 b2
>
> I get 0's for b. What I am doing wrong?
>
Well you have non-numerical values for b -- what is that supposed to mean?
-sven
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
5:59 p.m.
New subject: importing nominal variable
On Thu, 9 Feb 2012, Remigijus Lapinskas wrote:
>> Something went wrong with my gretl 1.9.7, Windows. When
importing
>> the ab.txt file
>>
>> a b
>> 1 b1
>> 2 b1
>> 3 b2
>>
>> I get 0's for b.
How exactly are you importing the data? I created a file named
ab.txt, containing the values you show above, and imported it
via /File/Open data/Import/"Text/CSV". The 'b' values were
coded as (1, 1, 2) as expected.
I also opened ab.txt via script and got the same result.
This is with current gretl CVS.
Allin Cottrell
6:35 p.m.
New subject: importing nominal variable
I reinstalled gretl from gretl-1.9.7.exe
<http://prdownloads.sourceforge.net/gretl/gretl-1.9.7.exe> from
http://gretl.sourceforge.net/win32/ on my Windows 7 for 64 bits. The
same result - all 0's.
Then I installed gretl from gretl_install.exe. Now it worked as expected.
Best, Rem
On 2012.02.09 19:59, Allin Cottrell wrote:
On Thu, 9 Feb 2012, Remigijus Lapinskas wrote:
>>> Something went wrong with my gretl 1.9.7, Windows. When importing
>>> the ab.txt file
>>>
>>> a b
>>> 1 b1
>>> 2 b1
>>> 3 b2
>>>
>>> I get 0's for b.
How exactly are you importing the data? I created a file named
ab.txt, containing the values you show above, and imported it
via /File/Open data/Import/"Text/CSV". The 'b' values were
coded as (1, 1, 2) as expected.
I also opened ab.txt via script and got the same result.
This is with current gretl CVS.
Allin Cottrell
_______________________________________________
Gretl-users mailing list
Gretl-users(a)lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users
7:41 p.m.
New subject: importing nominal variable
On Thu, 9 Feb 2012, Remigijus Lapinskas wrote:
I reinstalled gretl from gretl-1.9.7.exe
<http://prdownloads.sourceforge.net/gretl/gretl-1.9.7.exe> from
http://gretl.sourceforge.net/win32/ on my Windows 7 for 64 bits. The
same result - all 0's.
Then I installed gretl from gretl_install.exe. Now it worked as expected.
Ah, OK, thanks for the information.
Allin Cottrell
4699
days inactive
4758
days old
21 comments
8 participants
participants (8)
-
Allin Cottrell -
Dr RJF Hudson -
John C Frain -
Muheed Jamaldeen -
Remigijus Lapinskas -
Riccardo (Jack) Lucchetti -
Summers, Peter -
Sven Schreiber