Abstract
A new method for determining the lag order of the autoregressive polynomial in regression models with autocorrelated normal disturbances is proposed. It is based on a sequential testing procedure using conditional saddlepoint approximations and permits the desire for parsimony to be explicitly incorporated, unlike penalty-based model selection methods. Extensive simulation results indicate that the new method is usually competitive with, and often better than, common model selection methods.
Highlights
We consider the performance of a new method for selecting the appropriate lag order p of an autoregressive (AR) model for the residuals of a linear regression
The absolute sample correlations between each pair of the τi were all less than 0.02 for T = 15 and less than 0.013 for T = 30. These results are in stark contrast to the empirical distribution of the “t-statistics” and the associated p-values of the maximum likelihood estimates (MLEs)
We have operationalized the uniformly most powerful unbiased (UMPU) test for sequential lag order selection in regression models with autoregressive disturbances
Summary
We consider the performance of a new method for selecting the appropriate lag order p of an autoregressive (AR) model for the residuals of a linear regression. Besides the inherent problems involved in sequential testing procedures, such as controlling overall type I errors and the possible tendency to over-fit (as in backward regression procedures), the reliance on asymptotic distributions can be detrimental when working with small samples and unknown mean term Xβ. This latter problem could be overcome by using exact small-sample distribution theory and a sequence of point optimal tests in conjunction with some prior knowledge of the AR coefficients; see, e.g., King and Sriananthakumar (2015) and the references therein.
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