On Tuesday, 13 December 2011, Summers, Peter <
psummers@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@lists.wfu.edu [
gretl-users-bounces@lists.wfu.edu] on behalf of Dr RJF Hudson [
rjfhud@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@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@lists.wfu.edu<mailto:
gretl-users-bounces@lists.wfu.edu> [
gretl-users-bounces@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@highpoint.edu<mailto:
psummers@highpoint.edu><mailto:
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?
>
> From:
gretl-users-bounces@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@lists.wfu.edu<mailto:
gretl-users-bounces@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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