Wavelet Methods for Change-point Detection in Econometrics

Testing for structural breaks in economic and financial time series has been the subject of intense research. A considerable body of evidence has documented the instability of economic and financial time series. Common examples include the Phillip’s curve, interest rates and money demand. Modeling these unstable relationships has been an important challenge for applied econometricians. A large literature in econometrics is concerned with the methodological issues related to the identification, estimation, inference and forecasting in the presence of possible structural instability. The amount of work on this subject over the past several decades has been truly voluminous in the literatures of econometrics and statistics. At the same time, the recent development of wavelet analysis in applied mathematics has provided a new approach to constructing potentially powerful tests in econometrics. Wavelet's strength rests in its ability to localize time and scale simultaneously. At high scales, the wavelet’s small concentrated time support enables it to focus on short-lived phenomena, whereas at low scales, the wavelet’s large time support can identify long periodic behaviour. Wavelet can also zoom in on the behaviour of a process at a particular point in time, identifying singularities, jumps and cusps, by moving from low to high scales.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. This 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 for the purpose of obtaining the estimated residual errors. Also, with wavelet based tests, the researchers can determine the locations and sizes of the jump points. 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. The funding requested is for the hiring of a research assistant to carry out simulation experiments to investigate the small sample properties of the proposed tests and to construct empirical examples with real economic and financial data.