Comparison of AIC, BIC and AICC in autoregressive order 1 time series models

Abstract

Selecting a suitable model for a given data set from a set of competing models is known as statistical model selection. There are a number of model selection criteria such as Akaike’s Information Criterion (AIC), Bayesian Information Criterion (BIC) and Corrected Akaike’s Information Criterion (AICC). Even though it is crucial to choose a model that best fits a particular set of data, still there is no proper way to resolve this question. So, it is needed to find evidence to determine what is the best model selection criterion. The objective is to compare the most commonly used penalized model selection criteria namely AIC, BIC and AICC in the field of time series to determine the best performance criteria. This study mainly focus on Autoregressive models of order 1 (�� = Ø��−1 + �� �ℎ��� ��~��(0,1)) and investigate the performance of AIC, BIC and AICC for different scenarios. The behavior of these model selection criteria is examined and compared through Monte Carlo simulations. Here 500 series were simulated considering an Autoregressive model of order 1 for different sample sizes and different autoregressive coefficient values. The results of the simulation study are shown in bar graphs with the percentages of accurate selections and compared the performance of AIC, BIC and AICC. The study concludes that mostly BIC outperforms AIC and AICC for the considered scenarios.