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Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution

Author

Listed:
  • Yonghui Liu

    (School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China)

  • Guohua Mao

    (School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, China)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

  • Shuangzhe Liu

    (Faculty of Science and Technology, University of Canberra, Bruce, ACT 2617, Australia)

  • Alejandra Tapia

    (School of Engineering in Statistics, Universidad Católica del Maule, Talca 3466706, Chile)

Abstract

Autoregressive models have played an important role in time series. In this paper, an autoregressive model based on the skew-normal distribution is considered. The estimation of its parameters is carried out by using the expectation–maximization algorithm, whereas the diagnostic analytics are conducted by means of the local influence method. Normal curvatures for the model under four perturbation schemes are established. Simulation studies are conducted to evaluate the performance of the proposed procedure. In addition, an empirical example involving weekly financial return data are analyzed using the procedure with the proposed diagnostic analytics, which has improved the model fit.

Suggested Citation

  • Yonghui Liu & Guohua Mao & Víctor Leiva & Shuangzhe Liu & Alejandra Tapia, 2020. "Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:693-:d:353191
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    References listed on IDEAS

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    2. Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.
    3. S. Liu & T. Ma & A. SenGupta & K. Shimizu & M.-Z. Wang, 2017. "Influence Diagnostics in Possibly Asymmetric Circular-Linear Multivariate Regression Models," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 76-93, May.
    4. Carmichael, Benoıˆt & Coën, Alain, 2013. "Asset pricing with skewed-normal return," Finance Research Letters, Elsevier, vol. 10(2), pages 50-57.
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    1. Yuanyuan Ju & Yan Yang & Mingxing Hu & Lin Dai & Liucang Wu, 2022. "Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models," Mathematics, MDPI, vol. 10(8), pages 1-19, April.

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