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&gt;wrote: