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
>
>
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