Dimension reduction in high-dimensional multivariate time series analysis

The vector autoregressive (VAR) and vector autoregressive moving average (VARMA) models have been widely used to model multivariate time series, because of their ability to represent the dynamic relationships among variables in a system and their usefulness in forecasting unknown future values. This chapter explores the use of contemporal aggregation as a dimension reduction method, which is very natural and simple to use. Multivariate time series are of interest in many fields such as economics, business, education, psychology, epidemiology, physical science, geoscience, and many others. When modeling multivariate time series, the VAR and VARMA models are possibly the most widely used models, because of their capability to represent the dynamic relationships among variables in a system and their usefulness in forecasting unknown future values.