A Range-Based GARCH Model for Forecasting Volatility

Mapa, Dennis S. (2003): A Range-Based GARCH Model for Forecasting Volatility. Published in: The Philippine Review of Economics , Vol. XL, No. 2 (December 2003): pp. 73-90.

Abstract

A new variant of the ARCH class of models for forecasting the conditional variance, to be called the Generalized AutoRegressive Conditional Heteroskedasticity Parkinson Range (GARCH-PARK-R) Model, is proposed. The GARCH-PARK-R model, utilizing the extreme values, is a good alternative to the Realized Volatility that requires a large amount of intra-daily data, which remain relatively costly and are not readily available. The estimates of the GARCH-PARK-R model are derived using the Quasi-Maximum Likelihood Estimation (QMLE). The results suggest that the GARCH-PARK-R model is a good middle ground between intra-daily models, such as the Realized Volatility and inter-daily models, such as the ARCH class. The forecasting performance of the models is evaluated using the daily Philippine Peso-U.S. Dollar exchange rate from January 1997 to December 2003.

• Item Type: MPRA Paper
• Language: English
• Keywords: Volatility, Parkinson Range, GARCH-PARK-R, QMLE
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models ; Multiple Variables > C32 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics

References

Andersen T.G. and Bollerslev, T. (1998), “Answering the Skeptics: Yes, Standard Volatility Models do Provide Accurate Forecasts”, International Economic Review, 39, 885-905.

Andersen, T., Bollerslev, T., Diebold, F. X., and Labys, P., “The Distribution of Exchange Rate Volatility”, working paper 6961, National Bureau of Economic Research, February 1999.

Barndorff-Nielsen, O. E. and Shephard, N. (2002), “Estimating Quadratic Variation using Realized Variance”, Journal of Applied Econometrics, 17, 457-477.

Bollerslev, T. (1986), “Generalized Autoregressive Conditional Heteroskedasticity”, Journal of Econometrics, 31, 307-327. Bollerslev, T. and Wooldridge, J. M. (1992), “Quasi Maximum Likelihood Estimation and Inference in Dynamic Models with Time Varying Covariances”, Economic Reviews, 11, 143-172.

Busch, T., “Finite Sample Properties of GARCH Quasi-Maximum Likelihood Estimators and Related Test Statistics”, working paper, University of Aarhus, October 2003.

Campbell, J. Y., Lo, A. W., and Mackinlay, A. C. (1997), The Econometrics of Financial Markets. USA: Princeton University Press.

Chou, R. (2003), “Forecasting Financial Volatilities with Extreme Values: The Conditional Autoregressive Range (CARR) Model”, paper, Institute of Economics, Academia Sinica.

Ding, Z., Engle, R.F., and Granger, C. W. J. (1993) “Long Memory Properties of Stock Market Returns and a New Model”, Journal of Empirical Finance, 1, 83-106.

Engle, R. F. (1982), “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation”, Econometrica, 50, 987-1007.

Engle, R. F. (2002), “New Frontiers for ARCH Models”, Journal of Applied Econometrics, 17, 425-446.

Engle, R. F. and Gallo, G. (2003), “A Multiple Indicators Model for Volatility Using Intra-Daily Data”, working paper 10117, National Bureau of Economic Research, November 2003.

Engle, R. F. and Patton, A. J. (2001), “What Good is a Volatility Model?” unpublished manuscript, Department of Finance, Stern School of Business, New York University.

Engle, R. F. and Russell, J. (1998), “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data”, Econometrica, 66, 1127-1162.

Glosten, L. R., Jagannathan, R., and Runkle, D. (1993) “On the relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks”, Journal of Finance, 48, 1779-1801.

Hansen, P. and Lunde, A. (2001), “A Forecast Comparison of Volatility Models: Does anything Beat a GARCH (1,1)?”, working paper, Department of Economics, Brown University, November 2001.

Lee, S. and Hansen B. E. (1994), “Asymptotic Theory for the GARCH (1,1) Quasi-Maximum Likelihood Estimator”, Economic Theory, 10, 29-52.

Lumsdaine, R. L. (1996), “Consistency and Asymptotic Normality of the Quasi-Maximum Likelihood Estimator in IGARCH (1,1) and Covariance Stationarity GARCH (1,1) Models”, Econometrica, 64, 575, 596.

Nelson, D. (1991), “Conditional Heteroskedasticity in Asset Returns: A New Approach”, Econometrica, 59, 347-370.

Parkinson, M. (1980), “The Extreme Value Method for Estimating the Variance of the Rate of Return”, Journal of Business, 53, 61-65.

Taylor, J. W. (1999), “Evaluating Volatility and Interval Forecasts”, Journal of Forecasting, 18, 11-128.

Taylor, S.J. (1986), Modeling Financial Time Series. New York: John Wiley and Sons.