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Time Inhomogeneous Multiple Volatility Modeling

Author

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  • Wolfgang Hardle
  • Helmut Herwartz
  • Vladimir Spokoiny

Abstract

Price variations at speculative markets exhibit positive autocorrelation and cross correlation. Due to large parameter spaces necessary for joint modeling of variances and covariances, multivariate parametric volatility models become easily intractable in practice. We propose an adaptive procedure that identifies periods of second-order homogeneity for each moment in time. To overcome the high dimensionality of the problem we transform the multivariate series into a set of univariate processes. We discuss thoroughly the implementation of the adaptive technique. Theoretical and Monte Carlo results are given. We provide two applications of the new method. For a bivariate exchange rate series we compare the multivariate GARCH approach with our method and find the latter to be more in line with the underlying assumption of independently distributed innovations. Analyzing a 23-dimensional vector of asset returns we underscore the case for adaptive modeling in high-dimensional systems. , .

Suggested Citation

  • Wolfgang Hardle & Helmut Herwartz & Vladimir Spokoiny, 2003. "Time Inhomogeneous Multiple Volatility Modeling," Journal of Financial Econometrics, Oxford University Press, vol. 1(1), pages 55-95.
    • Handle: RePEc:oup:jfinec:v:1:y:2003:i:1:p:55-95
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