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A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations

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Time Series Analysis and Forecasting (ITISE 2017)

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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Abstract

In recent years, it is seen in many time series applications that innovations are non-normal. In this situation, it is known that the least squares (LS) estimators are neither efficient nor robust and maximum likelihood (ML) estimators can only be obtained numerically which might be problematic. The estimation problem is considered newly through different distributions by the use of modified maximum likelihood (MML) estimation technique which assumes the shape parameter to be known. This becomes a drawback in machine data processing where the underlying distribution cannot be determined but assumed to be a member of a broad class of distributions. Therefore, in this study, the shape parameter is assumed to be unknown and the MML technique is combined with Huber’s estimation procedure to estimate the model parameters of autoregressive (AR) models of order 1, named as adaptive modified maximum likelihood (AMML) estimation. After the derivation of the AMML estimators, their efficiency and robustness properties are discussed through simulation study and compared with both MML and LS estimators. Besides, two test statistics for significance of the model are suggested. Both criterion and efficiency robustness properties of the test statistics are discussed, and comparisons with the corresponding MML and LS test statistics are given. Finally, the estimation procedure is generalized to AR(q) models.

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Author information

Authors and Affiliations

  1. Middle East Technical University, Ankara, Turkey

    Ayşen Dener Akkaya

  2. Cankaya University, Ankara, Turkey

    Özlem Türker Bayrak

Authors
  1. Ayşen Dener Akkaya
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  2. Özlem Türker Bayrak
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Corresponding author

Correspondence to Ayşen Dener Akkaya .

Editor information

Editors and Affiliations

  1. ETSIIT, University of Granada, Granada, Spain

    Ignacio Rojas

  2. CITIC-UGR and ETSIIT, University of Granada, Granada, Spain

    Héctor Pomares

  3. Faculty of Sciences, University of Granada, Granada, Spain

    Olga Valenzuela

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Akkaya, A.D., Bayrak, Ö.T. (2018). A New Estimation Technique for AR(1) Model with Long-Tailed Symmetric Innovations. In: Rojas, I., Pomares, H., Valenzuela, O. (eds) Time Series Analysis and Forecasting. ITISE 2017. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-96944-2_4

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