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(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>]
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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