# 10. Multivariate Time Series

1. Ngai Hang Chan

Published Online: 28 JAN 2011

DOI: 10.1002/9781118032466.ch10

## Time Series: Applications to Finance with R and S-Plus, Second Edition

#### How to Cite

Chan, N. H. (2010) Multivariate Time Series, in Time Series: Applications to Finance with R and S-Plus, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118032466.ch10

#### Author Information

1. The Chinese University of Hong Kong, Department of Statistics, Shatin, Hong Kong

#### Publication History

1. Published Online: 28 JAN 2011
2. Published Print: 13 SEP 2010

#### Book Series:

1. Wiley Series in Probability and Statistics

#### ISBN Information

Print ISBN: 9780470583623

Online ISBN: 9781118032466

## SEARCH

### Keywords:

• autocovariance function;
• multivariate ARMA process;
• multivariate time series;
• SPLUS;
• time series;
• VARMA model;
• vector AR (VAR) models

### Summary

This chapter provides a brief summary of multivariate time series which leads to the development of vector autoregressive and moving average (VARMA) models. As in the univariate case, we can define an extremely useful class of multivariate stationary processes {Xt} by requiring that {Xt} should satisfy a set of linear difference equations with constant coefficients. The chapter first focuses on the estimation of the mean vector and the autocovariance function, and then presents a detailed discussion of the multivariate ARMA processes. Next, it considers vector AR (or VAR) time series models. Most of the inferences on estimation and testing for VAR models are similar to those of the univariate case. It should be pointed out that VAR models work quite well in many of the financial and econometric applications. The chapter presents an example to illustrate the VAR features of SPLUS.

#### Controlled Vocabulary Terms

ARMA process; autocovariance function; S-Plus; time series; VAR