Detecting Level Shifts in Time Series

Abstract

This article demonstrates the difficulty that traditional outlier detection methods, such as that of Tsay, have in identifying level shifts in time series. Initializing the outlier/level-shift search with an estimated autoregressive moving average model lowers the power of the level-shift detection statistics. Furthermore, the rule employed by these methods for distinguishing between level shifts and innovation outliers does not work well in the presence of level shifts. A simple modification to Tsay's procedure is proposed that improves the ability to correctly identify level shifts. This modification is relatively easy to implement and appears to be quite effective in practice.

KEY WORDS:

• ARMA model
• ARIMA model
• Intervention
• Misspecification
• Outlier