On the correlations in linearized multivariate stochastic volatility models

In the analysis of multivariate stochastic volatility models, many estimation procedures begin by transforming the data, taking the logarithm of the squared returns to obtain a linear state space model. A well-known series representation links the correlations between elements of the observation error in the actual and linearized forms of the model. This note derives a closed-form expression for the series and explores its statistical implications. The results are illustrated by means of a moment-based estimator of the correlations that is obtained in the process.