Fitting Finite Order VAR Models to Infinite Order Processes
In the previous chapters, we have derived properties of models, estimators, forecasts, and test statistics under the assumption of a true model. We have also argued that such an assumption is virtually never fulfilled in practice. In other words, in practice, all we can hope for is a model that provides a useful approximation to the actual data generation process of a given multiple time series. In this chapter, we will, to some extent, take into account this state of affairs and assume that an approximating rather than a true model is fitted. Specifically, we assume that the true data generation process is an infinite order VAR process and, for a given sample size T, a finite order VAR(p) is fitted to the data.
KeywordsImpulse Response Order Process Asymptotic Standard Error Forecast Error Variance Multiple Time Series
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