Most research on time series analysis and forecasting is normally based on the assumption of no structural change, which implies that the mean and the variance of the parameter in the time series model are constant over time. However, when structural change occurs in the data, the time series analysis methods based on the assumption of no structural change will no longer be appropriate; and thus there emerges another approach to solving the problem of structural change. Almost all time series analysis or forecasting methods always assume that the structure is consistent and stable over time, and all available data will be used for the time series prediction and analysis. When any structural change occurs in the middle of time series data, any analysis result and forecasting drawn from full data set will be misleading. Structural change is quite common in the real world. In the study of a very large set of macroeconomic time series that represent the ‘fundamentals’ of the US economy, Stock and Watson (1996) has found evidence of structural instability in the majority of the series. Besides, ignoring structural change reduces the prediction accuracy. Persaran and Timmermann (2003), Hansen (2001) and Clement and Hendry (1998, 1999) showed that structural change is pervasive in time series data, ignoring structural breaks which often occur in time series significantly reduces the accuracy of the forecast, and results in misleading or wrong conclusions. This chapter mainly focuses on introducing the most common time series methods. The author highlights the problems when applying to most real situations with structural changes, briefly introduce some existing structural change methods, and demonstrate how to apply structural change detection in time series decomposition.
Gradient-based structural change detection for nonstationary time series M-estimation
