Recursive estimation of the multivariate EWMA process

Recursive estimation methods suitable for univariate GARCH models have been recently studied in the literature. They undoubtedly represent attractive alternatives to the standard non-recursive estimation procedures with many practical applications (especially in the context of high-frequency financial data). It might be truly advantageous to adopt numerically effective techniques that can estimate, monitor, and control such models in real time. The aim of this contribution is to extend this methodology to the multivariate EMWA process by applying general recursive estimation instruments. The multivariate exponentially weighted moving average (MEWMA) model is a particular modelling scheme advocated by RiskMetrics that is capable of predicting the current level of financial time series covolatilities. In particular, the suggested approach seems to be useful for various multivariate financial time series with (conditionally) correlated components. Monte Carlo experiments are performed in order to investigate statistic features of the proposed estimation algorithm. Moreover, an empirical financial analysis demonstrates its capability.