| 报告题目： | On Wavelet-based Testing For Serial Correlation of Unknown Form Using Fan's Adaptive Neyman Method |
| 报 告 人： | Dr Linyuan Li(李林元) |
| University of New Hampshire | |
| 报告时间： | 6月17日(周一)下午2:30-4:00 |
| 报告地点： | 九龙湖数学系第一报告厅 |
| 相关介绍： | 报告人简介：Dr Linyuan Li(李林元) obtained his BS degree in Mathematics from Xuzhou Normal University, MS degree in Mathematical Statistics from East China Normal University and Ph.D. degree in statistics from Michigan State University in 2002. He is an associate professor in the Department of Mathematics and Statistics at University of New Hampshire, USA. His research interests include theory and application of statistics, wavelets and their applications, and time series analysis. He currently serves as an associate editor for journal of Statistics and Probability Letter. 摘要：Test procedures for serial correlation of unknown form with wavelet methods are investigated in this paper. The new wavelet-based consistent tests are motivated using Fan,s (1996) canonical multivariate normal hypothesis testing model. In our framework, the test statistics rely on empirical wavelet coefficients of a wavelet-based spectral density estimator. We advocate the choice of the simple Haar wavelet function, since evidence demonstrates that the choice of the wavelet function is not critical. Under the null hypothesis of no serial correlation, the asymptotic distribution of a vector of empirical wavelet coefficients is derived, which is the multivariate normal distribution in the limit. The proposed test statistics present the serious advantage to be completely data-driven or adaptive, avoiding the need to select any smoothing parameters. Furthermore, under a suitable class of fixed alternatives, the wavelet-based methods are consistent against serial correlation of unknown form. The test statistics are expected to exhibit better power than current test statistics when the true spectral density displays significant spatial inhomogeneity, such as seasonal or business cycle periodicities. However, the convergence of the test statistics toward their respective asymptotic distributions is expected to be relatively slow. Thus, Monte Carlo methods are investigated to determine the corresponding critical values. In a small simulation study, the new methods are compared with several test statistics, with respect to their exact levels and powers. |
