Bootstrap-based ARMA order selection

Abstract

Modelling the underlying stochastic process is one of the main goals in the study of many dynamic phenomena, such as signal processing, system identification and time series. The issue is often addressed within the framework of ARMA (Autoregressive Moving Average) paradigm, so that the related task of identification of the 'true' order is crucial. As it is well known, the effectiveness of such an approach may be seriously compromised by misspecification errors since they may affect model capabilities in capturing dynamic structures of the process. As a result, inference and empirical outcomes may be heavily misleading. Despite the big number of available approaches aimed at determining the order of an ARMA model, the issue is still open. In this paper, we bring the problem in the framework of bootstrap theory in conjunction with the information-based criterion of Akaike (AIC), and a new method for ARMA model selection will be presented. A theoretical justification for the proposed approach as well as an evaluation of its small sample performances, via simulation study, are given.

Bootstrap order selection for SETAR models

“…In fact, for T=500, smaller discrepancies (in average around 12.4%) has been recorded in the frequency of selection of the correct model. Such a behavior is consistent with our findings on the asymptotic equivalence of AIC and its bootstrap counterpart for ARM A models [10] and, Our method seems to increase AIC's selection performances, especially when processes show a strong structure, as in the case of DGP s 5 and 6. Averaging over these processes, our procedure picks the correct model 71.3% of the time versus 54.2% of the standard procedure for T=100 whereas for T=500 these percentages rise up to 81.7% and 72.6% respectively.…”

“…By comparing the two graphs, noticeable discrepancies can be observed between the two distributions along with a tendency to overestimation in the case of the small sample size. Such discrepancies appear to be less pronounced for T=500 and may be an indication of an asymptotic equivalence between the AIC for SET AR models and its bootstrapped counterpart, already verified in the ARMA case [10].…”

“…Therefore, in this paper we present a bootstrap selection criterion designed for the purpose of statistical-based identification of the "best" model in a set of non nested candidate models belonging to the class SET AR. As it will be seen, the method relies on a bootstrapped version of the Minimum Akaike Information Criterion Estimate (henceforth MAICE) procedure [1], already successfully tested in F o r P e e r R e v i e w O n l y the case of linear ARMA processes [10].…”

Bootstrap Order Determination for ARMA Models: A Comparison between Different Model Selection Criteria

“…This issue has attracted a lot of attention so that, according to different philosophies, theoretical and practical assumptions as well as several methods, both parametric and nonparametric, have been proposed over the years as a result. Among them, bootstrap strategies [5][6][7][8][9] are gaining more and more acceptance among researchers and practitioners.…”

A Genetic Algorithm Approach for Prediction of Linear Dynamical Systems

“…In case of transfer functions, autoregressive (AR), moving-average (MA), or autoregressive moving-average (ARMA) processes are the results of the modelling process of the physical and real-life problems (Wahlberg et al [4], AbdulRahim et al [5], and Dahlen [6]). The previous models play an important role in system identification and have a wide range of applications such as communication, signal processing, control systems, biomedical engineering, image processing and compression, prediction of spectrum estimation, and controlling of dynamic systems (Fenga and Politis [7], Broersen and de-Waele [8]).…”