Multivariate Time Series Analysis and Applications

10Dimension 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. However, when the number of dimensions is very large, the number of parameters often exceeds the number of available observations, and it is impossible to estimate the parameters. A suitable solution is clearly needed. In this chapter, after introducing some existing methods, we will suggest the use of contemporal aggregation as a dimension reduction method, which is very natural and simple to use. We will compare our proposed method with other existing methods in terms of forecast accuracy through both simulations and empirical examples.

10.1 Introduction

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. These models are described in many time series textbooks including Hannan (1970), Hamilton (1994), Reinsel (1997), Wei (2006), Lütkepohl ...