Adaptive Modeling and Forecasting for High-Dimensional Time Series

Abstract

With the fast advances in computing technologies, high-dimensional time series data have widely emerged in various areas, such as economics, bioscience, engineering, etc. Therefore, multivariate and high-dimensional time series modeling naturally attracts massive research and empirical interest; and simultaneously, non-stationarity becomes an inevitable issue to deal with in order to achieve desirable estimation and forecasting performance. In this thesis, we are motivated to propose three adaptive models to analyze and forecast high-dimensional time series under the existence of non-stationarity. The proposed models include factor model approach, adaptive multivariate approach and functional approach. In the factor model approach, a data-driven technology is proposed to automatically select a trustable stationary time interval such that the accuracy of forecasting is improved, compared with the benchmark competitor. In the multivariate and functional approach, the adaptive framework of the local univariate model is extended to both multivariate and functional domains. Especially, in the functional approach, a consistent maximum likelihood estimator for the functional autoregressive model with nonzero mean function is derived. Besides, with time-varying parameters, the adaptive functional approach can be safely applied to both stationary and non-stationary functional time series. Simulation study and real data applications are conducted for each of the proposed models. Reasonable and inspiring results are achieved in comparison with existing benchmark models.