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Time Inhomogeneous Multiple Volatility Modeling

  • Wolfgang Hardle
  • Helmut Herwartz
  • Vladimir Spokoiny

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. , .

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Article provided by Society for Financial Econometrics in its journal Journal of Financial Econometrics.

Volume (Year): 1 (2003)
Issue (Month): 1 ()
Pages: 55-95

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Handle: RePEc:oup:jfinec:v:1:y:2003:i:1:p:55-95
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  1. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Bollerslev, Tim & Engle, Robert F, 1993. "Common Persistence in Conditional Variances," Econometrica, Econometric Society, vol. 61(1), pages 167-86, January.
  3. Liptser, R. & Spokoiny, Vladimir G., 1999. "Deviation probability bound for martingales with applications to statistical estimation," SFB 373 Discussion Papers 1999,85, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  5. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  6. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  7. Engle, Robert F & Ito, Takatoshi & Lin, Wen-Ling, 1990. "Meteor Showers or Heat Waves? Heteroskedastic Intra-daily Volatility in the Foreign Exchange Market," Econometrica, Econometric Society, vol. 58(3), pages 525-42, May.
  8. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
  9. H. Herwartz, 1998. "Structural Analysis of Portfolio Risk Using Beta Impulse Response Functions," SFB 373 Discussion Papers 1998,41, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  10. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
  11. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
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