Distribution Based Level Change Detection in a Random Level Forecasting Model

Abstract

It is well known that an unexpected level change in time series can cause persistent forecasting errors, depending on the change size and the underlying time series process. This relationship is demonstrated particularly with macroeconomic and financial time series. Forecasting literature suggests using the relevant test statistics to detect the level change, but they are just measures that are not coupled with the correct statistical distributions. Hence, this study aims to find the correct statistical distribution of the level change statistic and to adapt the forecasting equation accordingly. The performance of the proposed method is validated by simulated time series and two empirical examples.