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Analysis of Financial Time Series, Third Edition by RUEY S. TSAY

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8.2 Vector Autoregressive Models

A simple vector model useful in modeling asset returns is the vector autoregressive (VAR) model. A multivariate time series Inline is a VAR process of order 1, or VAR(1) for short, if it follows the model

8.8 8.8

where Inline is a k-dimensional vector, Inline is a k × k matrix, and Inline is a sequence of serially uncorrelated random vectors with mean zero and covariance matrix Inline. In application, the covariance matrix Inline is required to be positive definite; otherwise, the dimension of Inline can be reduced. In the literature, it is often assumed that Inline is multivariate normal.

Consider the bivariate ...

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