Lecture 4 : Asymptotic Distribution

In time series analysis, we usually use asymptotic theories to derive joint distributions of the estimators for parameters in a model. Asymptotic distribution is a distribution we obtain by letting the time horizon (sample size) go to infinity. We can simplify the analysis by doing so (as we know that some terms converge to zero in the limit), but we may also have a finite sample error. Hopefully, when the sample size is large enough, the error becomes small and we can have a satisfactory approximation to the true or exact distribution. The reason that we use asymptotic distribution instead of exact distribution is that the exact finite sample distribution in many cases are too complicated to derive, even for Gaussian processes. Therefore, we use asymptotic distributions as alternatives.