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Forecasting financial volatility with combined QML and LAD-ARCH estimators of the GARCH model

  • John Galbraith
  • Liam Cheung

GARCH models and their variants are usually estimated using quasi-Maximum Likelihood (QML). Recent work has shown that by using estimates of quadratic variation, for example from the daily realized volatility, it is possible to estimate these models in a different way which incorporates the additional information. Theory suggests that as the precision of estimates of daily quadratic variation improves, such estimates (via LAD- ARCH approximation) should come to equal and eventually dominate the QML estimators. The present paper investigates this using a five-year sample of data on returns from all 466 S&P 500 stocks which were present in the index continuously throughout the period. The results suggest that LAD-ARCH estimates, using realized volatility on five-minute returns over the trading day, yield measures of 1-step forecast accuracy comparable or slightly superior to those obtained from QML estimates. Combining the two estimators, either by equal weighting or weighting based on cross-validation, appears to produce a clear improvement in forecast accuracy relative to either of the two different forecasting methods alone.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2013s-19.

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Length: 19 pages
Date of creation: 01 Jul 2013
Date of revision:
Handle: RePEc:cir:cirwor:2013s-19
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  1. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  2. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
  3. Zernov, Serguei & Zinde-Walsh, Victoria & Galbraith, John W., 2009. "Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 497-508, March.
  4. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  6. Bernard Bollen & Brett Inder, 1999. "Estimating Daily Volatility in Financial Markets Utilizing Intraday Data," Working Papers 1999.01, School of Economics, La Trobe University.
  7. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  8. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  9. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
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