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A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations

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  • Leila Sakhabakhsh
  • Rahman Farnoosh
  • Afshin Fallah
  • Mohammadhassan Behzadi

Abstract

The nonlinear autoregressive models under normal innovations are commonly used for nonlinear time series analysis in various fields. However, using this class of models for modeling skewed data leads to unreliable results due to the disability of these models for modeling skewness. In this setting, replacing the normality assumption with a more flexible distribution that can accommodate skewness will provide effective results. In this article, we propose a partially linear autoregressive model by considering the skew normal distribution for independent and dependent innovations. A semiparametric approach for estimating the nonlinear part of the regression function is proposed based on the conditional least squares approach and the nonparametric kernel method. Then, the conditional maximum‐likelihood approach is used to estimate the unknown parameters through the expectation‐maximization (EM) algorithm. Some asymptotic properties for the semiparametric method are established. Finally, the performance of the proposed model is verified through simulation studies and analysis of a real dataset.

Suggested Citation

  • Leila Sakhabakhsh & Rahman Farnoosh & Afshin Fallah & Mohammadhassan Behzadi, 2022. "A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlamp:v:2022:y:2022:i:1:n:7863474
    DOI: 10.1155/2022/7863474
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    References listed on IDEAS

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    1. M. Sharafi & A. R. Nematollahi, 2016. "AR(1) model with skew-normal innovations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 1011-1029, November.
    2. B. Tarami & M. Pourahmadi, 2003. "Multi‐variate t Autoregressions: Innovations, Prediction Variances and Exact Likelihood Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 739-754, November.
    3. Yu, Zhuoxi & Wang, Dehui & Shi, Ningzhong, 2009. "Semiparametric estimation of regression functions in autoregressive models," Statistics & Probability Letters, Elsevier, vol. 79(2), pages 165-172, January.
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    1. M. Alejandro Dinamarca & Fernando Rojas & Claudia Ibacache-Quiroga & Karoll González-Pizarro, 2025. "Modeling Time Series with SARIMAX and Skew-Normal and Zero-Inflated Skew-Normal Errors," Mathematics, MDPI, vol. 13(11), pages 1-23, June.

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