This thesis studies the statistical inferences for two representative classical multivariate time series models with heavy-tailed innovations: multivariate autoregressive moving average (ARMA) models and vector error correction (VEC) models. The asymptotic theories of the trace Whittle estimator of ARMA model and the least squares estimators (LSE) of VEC model are given. Meanwhile, this is the first time to reveal the relationship of tail index to limiting distribution and convergence rate of the above estimators, especially, for VEC model, the result is surprising and never observed in the literature which is further verified by some simulations studies. Besides the two models, this thesis also investigates testing and estimation of change-point in mean of general dependent da...[ Read more ]

This thesis studies the statistical inferences for two representative classical multivariate time series models with heavy-tailed innovations: multivariate autoregressive moving average (ARMA) models and vector error correction (VEC) models. The asymptotic theories of the trace Whittle estimator of ARMA model and the least squares estimators (LSE) of VEC model are given. Meanwhile, this is the first time to reveal the relationship of tail index to limiting distribution and convergence rate of the above estimators, especially, for VEC model, the result is surprising and never observed in the literature which is further verified by some simulations studies. Besides the two models, this thesis also investigates testing and estimation of change-point in mean of general dependent data (even heavy-tailed data) where trimmed self-normalized (SN) test and trimmed least squares estimation are deeply analysed. Simulation studies and two real examples are given to show the efficiency and robustness of our trimmed method.