STATISTICAL MODELING FOR HIGH-DIMENSIONAL AND NON-STATIONARY TIME SERIES

Abstract

In this thesis, we focus on statistical modelling, estimating and forecasting of the dynamic evolution of complex time series with high-dimensionality, special features and non-stationarity using the rich information contained in the large scale dataset. We have proposed and studied three models: the pFAR (the regularised partially functional autoregressive model), the ALG model (adaptive log-linear zero-inflated generalised Poisson autoregressive model with exogenous variable) and the AMS (adaptive multi-stage model), to describe the dynamic behaviour of functional time series with high-dimensional mixed-type covariates, non-stationary integer-valued time series with the features of autocorrelation, heteroscedasticity, over-dispersion and excessive number of zero observations, and time-inhomogeneous volatility process of financial return series respectively. We perform simulation studies to investigate the finite sample performance of the proposed models and demonstrate the applications to real word data.