Analysis of Financial Time Series, Third Edition

10.6 Factor–Volatility Models

Another approach to simplifying the dynamic structure of a multivariate volatility process is to use factor models. In practice, the “common factors” can be determined a priori by substantive matter or empirical methods. As an illustration, we use the factor analysis of Chapter 8 to discuss factor–volatility models. Because volatility models are concerned with the evolution over time of the conditional covariance matrix of , where , a simple way to identify the “common factors” in volatility is to perform a principal component analysis (PCA) on ; see the PCA of Chapter 8. Building a factor–volatility model thus involves a three-step procedure:

• Select the first few principal components that explain a high percentage of variability in .
• Build a volatility model for the selected principal components.
• Relate the volatility of each ait series to the volatilities of the selected principal components.

The objective of such a procedure is to reduce the dimension but maintain an accurate approximation of the multivariate volatility.

Example 10.8

Consider again the ...