This project consists of three areas of research in econometrics: wavelet analysis in time series/dynamic panels; evaluation of out-of-sample forecasts for densities and confidence inter-vals; and asymptotic distribution theory for nonparametric entropy measures of serial dependence. Wavelet analysis provides natural tools for estimating the spectrum of an economic time series, which typically has peaks/spikes, due to strong autocorrelation, seasonality and business cycles. One example is heteroskedasticity and autocorrelation con-sistent (HAC) covariance estimation. The popular Andrews-Newey kernel methods tend to underestimate the peak (and so the HAC), leading to overrejection in testing, and too narrow confidence interval estimates. This project develops a class of wavelet-based HAC estimators. Some simulation studies show that for the size of tests, the wavelet estimators outperform their kernel counterparts, particularly when serial correlation is strong. Two substantive extensions are pursued. The first is to refine the wavelet HAC estimators via a nonparametric frequency-domain prewhitening pro-cedure. This provides a faster convergent and more stable alternative than the commonly used parametric vector autoregression (VAR) prewhitening. The second extension is wavelet HAC estimation for panel models. The cur-rent practice for kernel HAC estimation in panels uses a bandwidth depending only on the number of time periods. This project finds that for both kernels and wavelets, the optimal smoothing parameters in panels depend on both the numbers of time periods and individuals. Wavelets are also used to distinguish a trend-stationary time series from a unit root process and to test serial correlation of unknown form in panel models.
Omnibus procedures for evaluating out-of-sample density and intervals forecasts are developed using a generalized spectral ap-proach. These procedures are supplemented with a class of separate inference procedures that can reveal information on sources of suboptimal density- and intervals forecasts. Appli-cations to stock markets and foreign exchange markets evaluate a variety of popular density forecast models.
For a class of kernel-based smoothed nonparametric entropy measures of serial dependence, this project develops an asymptotic distribution theory and shows how it can be used to derive the limit distributions for the existing entropy measures in the literature. The project develops tests that are either not available in the literature or are asymptotically more powerful than the existing procedures. Entropy measures can be used to test the random walk hypothesis, evaluate density- forecast models, identify significant lags of a time series and check the adequacy of dynamic likelihood models.
