Performances of Various Order Selection Criteria for Autoregressive Process

Abstract

In most economic researches, the selection of autoregressive order based for an economic time series is an essential task. Specifically, many econometric testing procedures, for instance, all forms of linearity, unit root, cointegration and causality tests, require the determination of optimal lag length selection in the first place. This study investigates the performances of various order selection criteria in selecting order of autoregressive (AR) process via a simulation study. Some 1000 independent time series for each AR process of known orders are first simulated and then subjected to lag length selection using various order selection criteria. The major findings of this study are as follows: First, the performance of various criteria in correctly estimated the true AR order deteriorates as the order grows. Second, the performance of various criteria in correctly estimated the true AR order improves as sample size grows.  Third, Akaike’s information criterion family (AICC, AIC) and final prediction error (FPE) are superior to other criteria for sample of size not exceeding 150 observations. Fourth, Hannan-Quinn criterion (HQC) performs better than others for sample size larger than 150 observations. Fifth, Schwarz information criterion (SIC), and Bayesian information criterion (BIC) could be useful in cases whereby a parsimony order, rather than true order is of interest; while Akaike’s information criterion (AIC) and final prediction error (FPE) are better options to avoid autocorrelation in our ultimate results.