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Forecasting The Conditional Covariance Matrix Of A Portfolio Under Long-Run Temporal Dependence

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Author Info
Antonio Rubia (Universidad de Alicante)
Trino-Manuel Ñíguez (Universidad de Alicante)

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Abstract

Long-range persistence in volatility is widely modelled and forecasted in terms of the so-called fractional integrated models. These models are mostly applied in the univariate framework, since the extension to the multivariate context of assets portfolios, while relevant, is not straightforward. We discuss and apply a procedure which is able to forecast the multivariate volatility of a portfolio including assets with long-memory. The main advantage of this model is that it is feasible enough to be applied on large-scale portfolios, solving the problem of dealing with extremely complex likelihood functions which typically arises in this context. An application of this procedure to a portfolio of five daily exchange rate series shows that the out-of-sample forecasts for the multivariate volatility are improved under several loss-functions when the long-range dependence property of the portfolio assets is explicitly accounted for.

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Paper provided by Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) in its series Working Papers. Serie AD with number 2003-34.

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Length: 30 pages
Date of creation: Oct 2003
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Publication status: Published by Ivie
Handle: RePEc:ivi:wpasad:2003-34

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Related research
Keywords: Exchange Rates; Fractional Integration; Long Memory; MGARCH models; PCA;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications
F31 - International Economics - - International Finance - - - Foreign Exchange

References listed on IDEAS
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  1. Peter F. Christoffersen & Francis X. Diebold & Til Schuermann, 1998. "Horizon Problems and Extreme Events in Financial Risk Management," Center for Financial Institutions Working Papers 98-16, Wharton School Center for Financial Institutions, University of Pennsylvania. [Downloadable!]
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  2. Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990. "Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 213-237. [Downloadable!] (restricted)
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  3. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July. [Downloadable!] (restricted)
  4. Brooks, Chris, 2001. "A Double-Threshold GARCH Model for the French Franc/Deutschmark Exchange Rate," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 135-43, March.
  5. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  6. Vilasuso, Jon, 2002. "Forecasting exchange rate volatility," Economics Letters, Elsevier, vol. 76(1), pages 59-64, June. [Downloadable!] (restricted)
  7. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September. [Downloadable!] (restricted)
  8. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June. [Downloadable!] (restricted)
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  9. Beine, Michel & Laurent, Sebastien & Lecourt, Christelle, 2002. "Accounting for Conditional Leptokurtosis and Closing Days Effects in FIGARCH Models of Daily Exchange Rates," Applied Financial Economics, Taylor and Francis Journals, vol. 12(8), pages 589-600, August. [Downloadable!] (restricted)
  10. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  11. Lopez, Jose A, 2001. "Evaluating the Predictive Accuracy of Volatility Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 87-109, March.
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  12. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July. [Downloadable!] (restricted)
  13. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348. [Downloadable!] (restricted)
  14. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December. [Downloadable!] (restricted)
  15. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Herwartz, Helmut & Golosnoy, Vasyl, 2007. "Semiparametric Approaches to the Prediction of Conditional Correlation Matrices in Finance," Economics Working Papers 2007,23, Christian-Albrechts-University of Kiel, Department of Economics. [Downloadable!]
  2. Christian Conrad, 2007. "Non-negativity Conditions for the Hyperbolic GARCH Model," KOF Working papers 07-162, KOF Swiss Economic Institute, ETH Zurich. [Downloadable!]
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