Robust Methods for Detection of Shifts of the Innovation Variance of a Time Series

Abstract

Based on Pitman asymptotic relative efficiency and Monte Carlo studies of power functions, Shorack [29] concluded in the independent and identically distributed (i.i.d.) case that the most satisfactory tests for scale changes were the Box-Andersen test and the jack knife. Analogs of these two procedures are shown to have identical asymptotic properties when the observations follow a correctly identified autoregressive process. A Monte Carlo study indicates that the performance of these robust procedures is roughly the same as in the i.i.d. case. The difference between the two robust procedures seems slight. The Box-Andersen procedure does a better job of maintaining the stated significance level but it lags slightly behind the jack knife in power.

KEYWORDS:

• Autoregressive process
• Variance shift
• Robust test
• Jack knife
• Asymptotic distribution
• Monte Carlo