The Application of Atheoretical Regression Trees to Problems in Time Series Analysis

• Main Author: Rea, William Stanley
• Language: en
• Published: University of Canterbury. Mathematics and Statistics 2008
• Subjects: regression trees; structural breaks; long memory; time series
• Online Access: http://hdl.handle.net/10092/1715

This thesis applies Atheoretical Regression Trees (ART) to the problem of locating changes in mean in a time series where the number and location of those changes are unknown. We undertook an extensive simulation study into ART's performance on a range of time series. We found ART to be a useful addition to currently established structural break methodologies such as the CUSUM and that due to Bai and Perron. ART was found to be useful in the analysis of long time series which are not practical to analyze with the optimal procedure of Bai and Perron. ART was applied to a long standing problem in the analysis of long memory time series. We propose two new methods based on ART for distinguishing between true long memory and spurious long memory due to structural breaks. These methods are fundamentally different from current tests and procedures intended to discriminate between the two sets of competing models. The methods were subjected to a simulation study and shown to be effective in discrimination between simple regime switching models and fractionally integrated processes. We applied the new methods to 16 realized volatility series and concluded they were not fractionally integrated series. All 16 series had mean shifts, some of which could be identified with historical events. We applied the new methods to a range of geophysical time series and concluded they were not fractional Gaussian noises. All of the series examined had mean shifts, some of which could be identified with known climatic changes. We conclude that our new methods are a significant advance in model discrimination in long memory series.