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Efficient and robust estimation for autoregressive regression models using shape mixtures of skewt normal distribution

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  • Uchenna Chinedu Nduka

    (University of Nigeria)

Abstract

Multiple linear regression model based on normally distributed and uncorrelated errors is a popular statistical tool with application in various fields. But these assumptions of normality and no serial correlation are hardly met in real life. Hence, this study considers the linear regression time series model for series with outliers and autocorrelated errors. These autocorrelated errors are represented by a covariance-stationary autoregressive process where the independent innovations are driven by shape mixture of skew-t normal distribution. The shape mixture of skew-t normal distribution is a flexible extension of the skew-t normal with an additional shape parameter that controls skewness and kurtosis. With this error model, stochastic modeling of multiple outliers is possible with an adaptive robust maximum likelihood estimation of all the parameters. An Expectation Conditional Maximization Either algorithm is developed to carryout the maximum likelihood estimation. We derive asymptotic standard errors of the estimators through an information-based approximation. The performance of the estimation procedure developed is evaluated through Monte Carlo simulations and real life data analysis.

Suggested Citation

  • Uchenna Chinedu Nduka, 2022. "Efficient and robust estimation for autoregressive regression models using shape mixtures of skewt normal distribution," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1519-1551, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09872-8
    DOI: 10.1007/s11009-021-09872-8
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    References listed on IDEAS

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    1. Mostafa Tamandi & Ahad Jamalizadeh & Tsung-I Lin, 2019. "Shape mixtures of skew-t-normal distributions: characterizations and estimation," Computational Statistics, Springer, vol. 34(1), pages 323-347, March.
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    3. McDonald, James B., 1989. "Partially adaptive estimation of ARMA time series models," International Journal of Forecasting, Elsevier, vol. 5(2), pages 217-230.
    4. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
    5. Wong, Wing-Keung & Bian, Guorui, 2005. "Estimating parameters in autoregressive models with asymmetric innovations," Statistics & Probability Letters, Elsevier, vol. 71(1), pages 61-70, January.
    6. Liu, Chuanhai, 1997. "ML Estimation of the MultivariatetDistribution and the EM Algorithm," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 296-312, November.
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