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.

基于正态分布和不相关误差的多元线性回归模型是一种流行的统计工具，已广泛应用于各个领域。但是，在现实生活中很难满足这些正常性和无序列相关性的假设。因此，本研究考虑具有离群值和自相关误差的序列的线性回归时间序列模型。这些自相关错误是由协方差平稳自回归过程，其中独立创新由skew-的形状混合物从动表示吨正态分布。skew-的形状混合物吨正态分布是skew-的柔性延伸吨正常，并带有控制偏斜度和峰度的附加形状参数。利用该误差模型，可以对所有参数进行自适应鲁棒性最大似然估计，从而对多个异常值进行随机建模。开发了“期望条件最大化”算法来执行最大似然估计。我们通过基于信息的近似推导估计器的渐近标准误差。通过蒙特卡洛模拟和现实生活中的数据分析来评估开发的估计程序的性能。