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> 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] 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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