Robust estimation of a time series model with structural change

Abstract

A procedure for estimating a time series model with structural change is proposed. Nonparametric bootstrap (block bootstrap or AR sieve) is applied to a series of estimates obtained through a modified forward search (FS) algorithm. The FS algorithm is implemented with overlapping and independent blocks of time points. The procedure can mitigate the difficulty in estimating when there is a temporary structural change. The simulation study indicated robustness of estimates from the estimation method when temporary structural change is introduced into the model provided that the time series is fairly long. As the effect of structural change persists in a longer period, the robustness of the bootstrap methods is further emphasized. We also provided a procedure for detecting the structural change and the subsequent adjustment of the overall model if indeed, there is a structural change.

Keywords:

• nonparametric bootstrap
• ARIMA model
• structural change
• forward search

AMS Classification :

• 62G05
• 62G09
• 62G35