Adaptive estimation of autoregression models under long-tailed symmetric distribution


Yentür B., AKKAYA A., Bayrak Ö. T.

Communications in Statistics: Simulation and Computation, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2022
  • Doi Number: 10.1080/03610918.2022.2103568
  • Journal Name: Communications in Statistics: Simulation and Computation
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Applied Science & Technology Source, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Computer & Applied Sciences, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Keywords: Autoregressive models, Adaptive modified Maximum likelihood, Efficiency, Robustness, Hypothesis testing, LINEAR-REGRESSION MODEL, MAXIMUM-LIKELIHOOD, ROBUST ESTIMATION, PARAMETERS, LOCATION

Abstract

© 2022 Taylor & Francis Group, LLC.Non-normal innovations in autoregression models frequently occur in practice. In this situation, least squares (LS) estimators are known to be inefficient and non-robust, and maximum likelihood (ML) estimators need to be solved numerically, which becomes a daunting task. In the literature, the modified maximum likelihood (MML) estimation technique has been proposed to obtain the estimators of model parameters. While an explicit solution can be found via this method, the requirement of knowing the shape parameter becomes a drawback, especially in machine learning. In this study, we use the adaptive modified maximum likelihood (AMML) methodology, which combines the MML with Huber’s M-estimation so that this assumption is relaxed. The performance of the method in terms of efficiency and robustness is analyzed via simulation and compared to LS, MML and ML estimates that are obtained numerically via the Expectation Conditional Maximization (ECM) algorithm. Test statistics are proposed for the crucial parameters of the model. The results show that the AMML estimators are preferable in most of the settings according to the mean squared error (MSE) criterion and the test statistics based on AMML method are more robust than the others. Furthermore, both real life and synthetic data examples are given.