Сравнительный анализ устойчивости различных методов оценивания параметров билинейной авторегрессионной модели

Abstract

The purpose of this work is to compare various methods in evaluating parameters of a bilinear autoregressive model. Least squares estimate, least absolute deviations estimate and estimate based on the Huber function were used as the parameter estimates. Computer simulation was introduced to study the indicated estimates precision depending on probability distribution of the bilinear autoregressive model upgrading process. Probable distribution of the upgrading process was simulated by normal and uniform distributions, Student distribution with various degrees of freedom, Laplace distribution (double exponential distribution), and Tukey distribution known as the polluted normal distribution. Their mean square error served as the evaluation precision measure. Results of the conducted computational experiment showed that precision of three methods used in evaluating parameters of the bilinear autoregressive series significantly depended on probability distribution of the model upgrading process. In particular, it concerns the number of degrees of freedom of the Student distribution, as well as the Tukey distribution pollution share and amount. If the upgrading process possesses normal and uniform distributions, Student’s distribution with sufficiently high number of degrees of freedom, the least squares method works more efficiently. Estimate based on the Huber function and the least absolute deviations estimate are becoming more efficient compared to the least squares estimation for the Laplace distribution, with a decrease in the number of degrees of freedom --- for the Student distribution, and with an increase in the pollution share and amount --- for the Tukey distribution