Model Estimation, Selection, and Checking

Abstract

Model estimation, selection, and diagnostic checking are three interwoven components of time series analysis. If, within a specified class of nonlinear models, a particular linearity test statistics indicates that the DGP underlying an observed time series is indeed a nonlinear process, one would ideally like to be able to select the correct lag structure and estimate the parameters of the model. In addition, one would like to know the asymptotic properties of the estimators in order to make statistical inference. Moreover, it is evident that a good, perhaps automatic, order selection procedure (or criterion) helps to identify the most appropriate model for the purpose at hand. Finally, it is common practice to test the series of standardized residuals for white noise via a residual-based diagnostic test statistic.