VAR and log transform

[fboehlandt]

Hello everyone,
I am seeking to estimate a VAR or, more specifically, a VEC model from 4 level index series. Testing the residual series for heteroskedasticity and normality reveals that the coefficient estimates may not be unbiased. One way to deal with this is to log-transform the original series. However, both in terms of the cointegrating relationship as well as the short-term exposure to the lagged differenced series, the results are quite different from the estimates based on the level series. For example, the initial model proposed would include differenced lags from t - 1 to t - 3, a first-order cointegration relationship and 2 cointegrating equations. When using the log transformed series, often there appears to be no cointagrating relationship whatsoever (even though the individual processes are ~I(1)). This is surprising, since the cointegrating relationship for some of the series included is well establish in economic theory (an supported when the models are estimated form the non-transformed series). I include my questions:
- What estimation errors can be expected form log transformation of the original series? Can a log transform be justified?
- What alternatives exist to produce HAC-error estimates? There appears to be no option to select HAC errors in a VAR framework.
- What are the consequences of hetereoskedasticity and non-normality for model estimation according to multivariate estimation criterion suc has AIC and SBIC? I understand the coefficient estimates are still consistent though not unbiased.
Any feedback is greatly appreciated
Regards
Florian

[trubador]

What is the source of heteroscedasticity/nonnormality? Is it due to clusters in residuals or simply the result of nonstationarity in residuals? It would be helpful to see some output...

[fboehlandt]

Hello trubador,
thanks for your quick reply. I have included an example workbook for your convenience. As you can see, the data are four time series of index levels which are to be included as endogenous variables in a VAR. The data is non-stationary or ~I(1) process. There is evidence that the series are cointegrated. The model selected according to AIC:
- Rank of the cointegrating relationship: 1
- Intercept and trend in CE - no trend in VAR
- Lag interval for D: 1 3
I have tested for various restrictions in the adjustment coeffients as well as the parameters of the cointegrating vector. The restrictions of thecurrent model are:
A(1,1)=0,A(3,1)=0,B(1,4)=0

I don't know if the restrictions imposed have any bearing on the properties of the residual series, but I have included them here just in case. I was under the impression that if the model is correctly specified with respect to the cointegrating relationship and the first-differenced terms are used as the VAR components (i.e. a VEC), the residual series should not be non-stationary. I conclude thus that either:
- the model is not specified correctly
- the source of heteroskedasticity/nonnormality does not come about as a result of nonstationarity
I followed a structured approach in determining the appropriate model (since there is no economic theory suggestive of a particular model), so I suspect there is some margin of error when selecting the model. Maybe you can give some advice looking at the data yourself

[trubador]

The problem seems to be the structural change around 2008 (due to global financial crisis). Dynamics of the relationship you seek might have changed before and after this period, so you may want to control it via some sort of dummy variable at least. Extending the sample might also help, since you have only a few observations for the post-crisis period.

[fboehlandt]

Hello trubador,
I suspected as much. Unfortunately, the data for CTA is difficult to come by (i.e. more observations not really an option). I will try to include an exongenous dummy variable with August 2008 as a cut-off and report back. Thanks for your input

[fboehlandt]

Hi trubador,
removing the observations for months 2008M09 and 2008M10 using a dummy variable works. It is the GSCI series causing trouble. I also estimate the correct VEC using IC. I calculate the IC for various lag lengths and deterministic trend assumptions and record the results in a matrix. I don't know, however, if the IC are comparable across models. Can you advise please?

[trubador]

You can use information criteria to determine the underlying trend structure. Actually, EViews summarizes all five of the alternative specifications if you like. As for the lag length, lag exclusion tests are more appropriate.