On the correlations in linearized multivariate stochastic volatility models - Karim Moussa (Tinbergen Institute, 2025)
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 discusses its statistical implications. Additionally, it offers a new interpretation of the correlations in the linearized model.
Keywords: 330; Multivariate volatility models; Quasi-maximum likelihood; Cross-correlation