Pitfalls of fitting autoregressive models for heavy-tailed time series
This paper deals with the problem of application of autoregression models \(AR(p)\) to the analysis of heavy-tailed time series data. It focuses on two methods of parameter estimation: Yule-Walker (YW) and linear programming (LP). A brief overview of the methods of AR model selection and tests of AR model adequacy is presented. Ways of robustifying LP estimators are proposed. The main task of the paper is the investigation of the effects of misspecified models on AR estimation. The authors study what happens in two cases: (1) presence of outliers, (2) completeness of models when the model is really bilinear or finite order moving average. To illustrate the influence of nonlinearities and presence of outliers both simulated and real data sets are presented and analyzed. The results are discussed. The authors emphasize the fact that applications of AR models to real heavy-tailed data rarely occur to be successful. A warning is given against the assumption that autoregressions will be an appropriate class of models for fitting heavy-tailed data.
scientific article; zbMATH DE number 1408669
scientific article