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Abstract:
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The conditional variance, or squared volatility, of asset returns evolves over time; furthermore, financial volatilities move together over time across assets and markets. For even a handful of assets, the curse of dimensionality quickly makes estimation of most multivariate models impractical. We extend methods from Independent Component Analysis to effectively reduce the estimation problem to a set of disjoint univariate models. Our multivariate conditional heteroscedastic model allows exact or stochastic parameterizations, as well as asymmetry in the respective volatility series. Correlations evolve over time without explicit modeling, and the estimated volatility matrix is positive-definite at every time index.
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