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Correlated ARCH (CorrARCH): modelling the time-varying conditional correlation between financial asset returns. (English) Zbl 1159.91461
Summary: Although the time variation of the conditional correlations of asset returns is a well established stylized fact (and of crucial importance for efficient financial decisions) there is no explicit general model available for its estimation and forecasting. In this paper, we propose a bivariate GARCH covariance structure in which conditional variances can follow any GARCH-type process, while conditional correlation is generated by an explicit discrete-time stochastic process, the CorrARCH process. A high order CorrARCH can parsimoniously be represented by a CorGARCH process. The model successfully generates the reported stylized facts, establishes an autocorrelation structure for correlations and thus provides an explicit framework for out-of-sample forecasting. We provide empirical evidence from the G7 Stock Market Indexes.

MSC:
91B82 Statistical methods; economic indices and measures
91B84 Economic time series analysis
91G70 Statistical methods; risk measures
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