Diagnostics for a Linear Model with First-Order Autoregressive Symmetrical Errors

Abstract

In this article, we focus on some diagnostics for linear regression model with first-order autoregressive and symmetrical errors. The symmetrical class includes both light- and heavy-tailed univariate symmetrical distributions, which offers a more flexible framework for modeling. Maximum likelihood estimates are computed via the Fisher-score method. Score statistic and its adjustment are proposed for testing autocorrelation of the random errors. Local influence diagnostics are also derived for the model under some usual perturbation schemes. The performances of the test statistics are investigated through Monte Carlo simulations. Finally, a real data set is used to illustrate our diagnostic methods.

Keywords:

• AR(1) errors
• Diagnostics
• Linear model
• Local influence
• Score test
• Symmetrical distributions

Mathematics Subject Classification:

• 62J05
• 62J20

Acknowledgments

This research was supported by National Basic Research Program of China, Grant No. 2009CB426313, the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2012459), and Program Sponsored for Scientific Innovation Research of College Graduate in Jiangsu Province. We are grateful to the associate editor and referees for their helpful comments which largely improve our work. We also thank Dr. Lianhua Zhu for kindly supplying the weather data of our application.