报告题目：On Wavelet-based Testing For Serial Correlation of Unknown Form Using Fan’s Adaptive Neyman Method

报告人： Professor Linyuan LI(美国New Hampshire大学教授）

Abstract: 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. It is also shown that the wavelet coefficients are asymptotically uncorrelated. 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 local 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 has significant spatial inhomogeneity, such as seasonal or business cycle periodicities. However, the convergence of the test statistics toward their respective asymptotic distributions appears 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.

时间：2012年6月7日（周四）下午16:00开始

地点：数学系致远楼 102会议室