Hey,
As we all are doing modelling econometric methods towards stationary and non-stationary time series, I would like we can compile our views on steps to follow for selecting the best models among three stationary time series. The sources provide a lost of suggestions out there but here, lets compile our views and experiences in persona to compile these steps for better understanding of new econometricians like me. Thank you.
Hi Anees, your question is not very clear but I will give my answer based on what I believe you are asking for.
Modelling three stationary time series variables is a straight forward thing because the issue of unit root and co-integration will no longer poss a problem. The general thing in modelling is that your model selection depends on what you intend to use the model for. There is no "one cap fits all" model. It may be structural or non-structural, static or dynamic, theoretic or atheoretic.
If you are interested in impact analysis, you should go for a Structural model that may be static or dynamic and choose a better model among the available alternatives using the information criteria, likely the SIC criteria as it is the widely used. On the other hand, if you are interested in forecasting, it has been shown that dynamic models have better forecasting power compared to the static and structural ones. In this also, you will select the appropriate lag/lead length using the information criteria.
IF ALL VARIABLES ARE STATIONARY, THEN THE BASIC MODEL SELECTION RULES APPLY. THAT IS ADJUSTED R-SQUARED, AKAIKE INFORMATION CRITERIA, BIC AMONG OTHERS. THEN ONE ALSO HAVE TO CHECK THE BEHAVIOUR OF HIS DEPENDENT VARIABLE, WHETHER LAGGED VALUES SHOULD BE INCLUDED (ADF MODELS) OR IF GRANGER CAUSALITY TESTS ARE NEEDED BETWEEN VARIABLES. ALSO MISSPECIFICATION TEST ARE REQUIRED.
If you have multiple stationary time series data you can model them using VAR methodology that will allow you to perform impulse response analysis that you can use to assess monetary and fiscal policy stances. VAR methodology will allow you to identify monetary and fiscal policy shocks either using 'Choleskey decomposition method' or 'Structural VAR method' that allows you to impose economic theory driven restrictions on the 'contemporaneous relationships' among the variables in consideration. You can also use your estimated VAR model for baseline forecasting for the variables involved. Alternatively, you can model one stationary time series at a time with the aid of Box-Jenkins methodology (ARMA modeling).
You only choose among models not among variables. Chosing among models is relatively easy of each of the three models in nested in one general model. If not, there are several ways of testing, See Elements of Econometrics, 2nd ed. by Jan Kmenta
If all your variables are stationary at level then you have two options – (1) Static Model (2) Dynamic model. If you are interested in the direction of association among variables along with their strength then run a simple OLS. On the other hand, if your objective is to examine (short run) causal relationship (what causes what), go with VAR. In any case you need not unnecessarily check for co-integration.
The best model among several competing models (not variables--that is a wrong term) is one that nests all of them (see David Hendry's argument on this)
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