Multivariate Markov switching BEKK models: filtering, estimation and data analysis

This paper deals with an extension of the standard multivariate BEKK model, as detailed in Engle and Kroner (1995), by allowing both the unconditional correlation and the parameters to be driven by an unobservable Markov chain. We propose two estimation algorithms by using extended Kalman filters, derived from suitable state space representations of the considered model. Numerical examples make evident the effectiveness of the proposed nonlinear estimations. Moreover, real-data applications on some financial returns show empirical evidence that the high volatility persistence and correlation changes of such returns can be well explained by estimating multivariate Markov switching BEKK parameters via the two efficient proposed algorithms. Finally, such results are compared to those obtained using Markov switching CCC and DCC models from Billio and Caporin (2005) to analyze financial contagion in the stock market and value-at-risk forecasts.