Robust Estimation Procedure for Autoregressive Models with Heterogeneity

Abstract

In environmental studies, regression analysis is frequently performed. The classical approach is the ordinary least squares method which consists in minimizing the sum of the squares of the residuals. However, this method relies on strong assumptions that are not always satisfied. In environmental data, the response variable often contains outliers and errors can be heteroscedastic. This can have significant effects on parameter estimation. To solve this problem, the weighted M-estimation was developed. It assumes a parametric function for the variance, and, estimates alternately and robustly, mean and variance parameters. However, this method is limited to the independent errors case, and is not applicable to time series data. Therefore, we introduce a new estimation procedure which adapts the weighted M-estimation to environmental time series data, while selecting optimal value for the tuning parameter present in the M-estimation. We compare the efficiency of our procedure on simulated data to other usual regression methods. Our estimation procedure outperforms the other methods providing estimates with lower biases and mean squared errors. Finally, we illustrate the proposed method using an air quality dataset from Beijing. This method has been implemented in the R package RlmDataDriven.