Time Inhomogeneous Multiple Volatility Modeling

Price variations at speculative markets exhibit positive autocorrelationand cross correlation. Due to large parameter spaces necessaryfor joint modeling of variances and covariances, multivariateparametric volatility models become easily intractable in practice.We propose an adaptive procedure that identifies periods ofsecond-order homogeneity for each moment in time. To overcomethe high dimensionality of the problem we transform the multivariateseries into a set of univariate processes. We discuss thoroughlythe implementation of the adaptive technique. Theoretical andMonte Carlo results are given. We provide two applications ofthe new method. For a bivariate exchange rate series we comparethe multivariate GARCH approach with our method and find thelatter to be more in line with the underlying assumption ofindependently distributed innovations. Analyzing a 23-dimensionalvector of asset returns we underscore the case for adaptivemodeling in high-dimensional systems.