Herwartz, Helmut: Time Inhomogeneous Multiple Volatility Modelling
World Conference Econometric Society, 2000, Seattle

Wolfgang Haerdle, Humboldt Universitaet zu Berlin
Helmut Herwartz, Humboldt Universitaet zu Berlin
Volodia Spokoiny, Humboldt Universitaet zu Berlin
Time Inhomogeneous Multiple Volatility Modelling
Session: C-2-23  Saturday 12 August 2000  by Herwartz, Helmut
Price variations observed at speculative markets exhibit positive autocorrelation and cross correlation among a set of assets, stock market indices, exchange rates etc. A particular problem in investigating multivariate volatility processes arises from the high dimensionality implied by a simultaneous analysis of variances and covariances. Parametric volatility models as e.g. the multivariate version of the prominent GARCH model become easily intractable for empirical work. We propose an adaptive procedure that aims to identify periods of second order homogeneity for each moment in time. Similar to principal component analysis the dimensionality problem is solved by transforming a multivariate series into a set of univariate processes. We discuss thoroughly implementation issues which naturally arise in the framework of adaptive modelling. Theoretical and Monte Carlo results are given. The empirical performance of the new method is illustrated by an application to a bivariate exchange rate series. Empirical results are compared to a parametric approach, namely the multivariate GARCH model.
Submitted paper full-text in .pdf

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