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
----- Original Message -----
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>
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
[gretl-users-bounces@lists.wfu.edu]
on behalf of Muheed Jamaldeen [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>>
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?
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@lists.wfu.edu
http://lists.wfu.edu/mailman/listinfo/gretl-users