Bootstrap method for minimum message length autoregressive model order selection

Abstract

Minimum Message Length MML87 is an information theoretical criterion for model selection and point estimation. In principle, it is a method of inductive inference, and is used in a wide range of approximations and algorithm to determine the ideal model for any given data. In this study, MML87 model selection criterion was investigated and compared with other notably model selection criteria such as Akaike information criterion (AIC), Bayesian information criterion (BIC), Corrected Akaike information criterion (AICc), and Hannan-Quinn (HQ), using Bootstrap Simulation Technique to simulate autoregressive model of order P. We specified three different counts systems as under inferred, correctly inferred and over inferred. Based on the candidate model explored with autoregressive model and the aggregate true model explored, with the estimated parameters. MML87 performed better than all other model selection criteria through the negative log likelihood function and the mean square prediction error estimated. It is more efficient and correctly inferred.

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“…All time series were analyzed for stationarity using the ADF test [ 81 , 82 ], taking into account the optimal number of lags. The optimal number of lags was determined based on the information criteria of the final prediction error (FPE) [ 83 , 84 ], Akaike (AIC) [ 85 , 86 ], Schwarz (SC) [ 87 ], and Hannan–Quinn (HQ) [ 88 , 89 , 90 ]. If the stationarity of the time series was not confirmed, the study was supplemented with a cointegration test, the so-called Johansen trace test [ 33 , 82 , 91 ].…”