Model selection uncertainties and model averaging in autoregressive time series models

Abstract

Selecting the correct lag order is necessary in order to avoid model specification errors in autoregressive (AR) time series models. Here we explore the problem of lag order selection in such models. This study provides an in-depth but easy understanding of the model selection mechanism to the practitioners in various fields of applied research. Several interesting findings are reported and through these the pitfalls of the model selection procedures are exposed. In particular, we show that the whole exercise of model selection and subsequent statistical inference invariably depends upon unknown entities, namely the true values of parameters in the model. The model averaging technique is proposed as an alternative to the common practice of model selection and it is shown that, as a result, the properties of post-model-selection estimates substantially improve.