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Real-Time Multivariate Density Forecast Evaluation and Calibration: Monitoring the Risk of High-Frequency Returns on Foreign Exchange

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Author Info
Francis X. Diebold
Jinyong Hahn
Anthony S. Tay

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Abstract

We provide a framework for evaluating and improving multivariate density forecasts. Among other things, the multivariate framework lets us evaluate the adequacy of density forecasts involving cross-variable interactions, such as time-varying conditional correlations. We also provide conditions under which a technique of density forecast "calibration" can be used to improve deficient density forecasts. Finally, motivated by recent advances in financial risk management, we provide a detailed application to multivariate high-frequency exchange rate density forecasts.

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Publisher Info
Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 98-079.

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Date of creation: 26 Aug 1998
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Handle: RePEc:fth:nystfi:98-079

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Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
Web page: http://w4.stern.nyu.edu/finance/
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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. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  2. Soderlind, Paul & Svensson, Lars, 1997. "New techniques to extract market expectations from financial instruments," Journal of Monetary Economics, Elsevier, vol. 40(2), pages 383-429, October. [Downloadable!] (restricted)
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  3. Francis X. Diebold & Jose A. Lopez, 1996. "Forecast Evaluation and Combination," NBER Technical Working Papers 0192, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  4. Chatfield, Chris, 1993. "Calculating Interval Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 121-35, April.
  5. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June. [Downloadable!] (restricted)
  6. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August. [Downloadable!] (restricted)
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  7. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-65, September. [Downloadable!] (restricted)
  8. Chatfield, Chris, 1993. "Calculating Interval Forecasts: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(2), pages 143-44, April.
  9. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  10. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  11. Clements, M.P. & Smith J., 1998. "Evaluating The Forecast of Densities of Linear and Non-Linear Models: Applications to Output Growth and Unemployment," The Warwick Economics Research Paper Series (TWERPS) 509, University of Warwick, Department of Economics.
  12. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113. [Downloadable!] (restricted)
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  13. Francis X. Diebold & Anthony S. Tay & Kenneth F. Wallis, 1997. "Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters," NBER Working Papers 6228, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  14. Tim Bollerslev & Robert F. Engle & Daniel B. Nelson, 1993. "ARCH Models," University of California at San Diego, Economics Working Paper Series 93-49, Department of Economics, UC San Diego. [Downloadable!]
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    • Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier. [Downloadable!] (restricted)
  15. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques. [Downloadable!]
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  16. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  17. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
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(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. Jose A. Lopez & Marc R. Saidenberg, 1999. "Evaluating credit risk models," Working Papers in Applied Economic Theory 99-06, Federal Reserve Bank of San Francisco. [Downloadable!]
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