Adaptive estimation of autoregressive models under long-tailed symmetric distribution

Date

2019-07-08

Author

Yentür, Begüm
Bayrak, Özlem Türker
Akkaya, Ayşen

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In this paper, we consider the autoregressive models where the error term is non-normal; specifically belongs to a long-tailed symmetric distribution family since it is more relevant in practice than the normal distribution. It is known that least squares (LS) estimators are neither efficient nor robust under non-normality and maximum likelihood (ML) estimators cannot be obtained explicitly and require a numerical solution which might be problematic. In recent years, modified maximum likelihood (MML) estimation is developed to overcome these difficulties. However, this method requires that the shape parameter is known which is not realistic in machine data processing. Therefore, we use adaptive modified maximum likelihood (AMML) technique which combines MML with Huber's estimation procedure so that the shape parameter is also estimated. After derivation of the AMML estimators, their efficiency and robustness properties are discussed through a simulation study and compared with MML and LS estimators.

Subject Keywords

Mathematics of computing, Probability and statistics, Probabilistic inference problems, Statistical paradigms, Regression analysis, Time series analysis

URI

https://hdl.handle.net/11511/33104

DOI

https://doi.org/10.1145/3343485.3343490

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Department of Statistics, Conference / Seminar

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Citation Formats

B. Yentür, Ö. T. Bayrak, and A. Akkaya, “Adaptive estimation of autoregressive models under long-tailed symmetric distribution,” 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/33104.