(1) Preliminary Test Estimation for Regression Models with Long-Memory Disturbance (2) Jackknifed Whittle Estimators

Abstract

(1) For a class of time series regression models with long-memory disturbance, we are interested in estimation of a subset of the regression coefficient vector and spectral parameter of the residual process when the complementary subset is suspected to be close to 0. In this situation we evaluate the mean square errors of the restricted and unrestricted MLE and a preliminary test estimator when the complementary parameters are contiguous to zero vector. The results are expressed in terms of the regression spectra and the residual spectra. Since we assume long-memory dependence for the disturbance, the asymptotics are much different from the case of i.i.d. disturbance. Numerical studies elucidate some interesting features of regression and long-memory structures. (This is a joint work with Hiroaki Ogata and Hiroshi Shiraishi.)?? Keywords: Time regression model; long-memory process; fractional spectral density; LAN theorem; restricted MLE; unrestricted MLE; preliminary test estimator. (2) The Whittle estimator has been widely used in time series analysis. Although it is Gaussian asymptotically efficient, it suffers from large bias, especially, when the process concerned has near unit roots. In this paper we introduce the jackknife technique to the Whittle likelihood in the frequency domain, and elucidate the asymptotics of the Jackknifed Whittle estimator. For non-Gaussian stationary processes, it is shown that the second-order bias of it vanishes when the unknown parameter is innovation-free. Some numerical studies confirm the theoretical results. Because the Whittle estimator is applicable to many fields, e.g., natural sciences, signal processing and econometrics, use of the bias-reduced Jackknifed Whittle estimator is profitable. (This is a joint work with K. Tamaki, T. DiCiccio and A. C. Monti.) Keywords: Asymptotic efficiency; Innovation-free; Jackknife estimator; Second-order bias; Spectral density; Stationary process; Whittle estimator.