Wavelet Methods for Change-point Detection in Econometrics

The main purpose of this project is to introduce a new approach to the analysis of jumps and sharp cusps in a non-parametric regression using wavelet analysis. The model set-up allows for correlations in the observations and errors. Unlike common existing econometric tests, wavelet-based tests do not require the complicated estimation of conditional heteroscedastic variance to obtain the estimated residual errors. Also, with wavelet-based tests, the locations and sizes of the jump points can be determined. A large amount of the theoretical work for the project has in fact been completed. One enlightening aspect of the results obtained is that the proposed tests have a convenient limiting N(0,1) distribution. This is in contrast to a recently published related work, which approaches the testing problem somewhat differently with the resultant test statistic converging to a (non-standard) extreme value distribution. Theoretical analysis of multiple jump points is yet to be conducted. Simulation experiments will be carried out to investigate the small sample properties of the proposed tests and to construct empirical examples with real economic and financial data.