Estimation and inference for multivariate heavey-tailed and threshold time series models

Abstract

This thesis considers multivariate heavy-tailed nonstationary time series models and the structure-changed threshold double autoregressive (TDAR) models. The first part develops an automated approach to determine the cointegrating rank, lag order and estimate parameters simultaneously in the vector error correction (VEC) model with heavy-tailed innovations. In the second part, the asymptotic theories of the full rank least squares estimator (FLES) and reduced rank least squares estimator (RLSE) of heavy-tailed and nonstationary autoregressive and moving average (ARMA) models are given. This thesis also investigates the asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of structure changed and two-regime TDAR models. It is shown that both the estimated threshold and change-point are n-consistent, and they converge weakly to the smallest minimizer of a compound Poisson process and the location of minima of a two-sided random walk, respectively. Simulation studies and real examples are given to evaluate the performance of our methods.