The one-trading-day-ahead forecast errors of intra-day realized volatility

Degiannakis, Stavros (2017): The one-trading-day-ahead forecast errors of intra-day realized volatility. Published in: Research in International Business and Finance No. 42 (2017): pp. 1298-1314.

Abstract

Two volatility forecasting evaluation measures are considered; the squared one-day-ahead forecast error and its standardized version. The mean squared forecast error is the widely accepted evaluation function for the realized volatility forecasting accuracy. Additionally, we explore the forecasting accuracy based on the squared distance of the forecast error standardized with its volatility. The statistical properties of the forecast errors point the standardized version as a more appropriate metric for evaluating volatility forecasts. We highlight the importance of standardizing the forecast errors with their volatility. The predictive accuracy of the models is investigated for the FTSE100, DAX30 and CAC40 European stock indices and the exchange rates of Euro to British Pound, US Dollar and Japanese Yen. Additionally, a trading strategy defined by the standardized forecast errors provides higher returns compared to the strategy based on the simple forecast errors. The exploration of forecast errors is paving the way for rethinking the evaluation of ultra-high frequency realized volatility models.

• Item Type: MPRA Paper
• Language: English
• Keywords: ARFIMA model, HAR model, intra-day data, predictive ability, realized volatility, ultra-high frequency modelling.
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; 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 > C50 - General; G - Financial Economics > G1 - General Financial Markets > G11 - Portfolio Choice ; Investment Decisions; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets

References

Aït-Sahalia, Y., Mykland, P.A. and Zhang, L. (2005). How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise. Review of Financial Studies, 18, 351–416.

Aït-Sahalia, Y., Mykland, P.A. and Zhang, L. (2011). Ultra-High Frequency Volatility Estimation with Dependent Microstructure Noise, Journal of Econometrics, 160, 190-203.

Akaike, H. (1973). Information Theory and an Extension of the Maximum Likelihood Principle. Proceedings of the second international symposium on information theory. B.N. Petrov and F. Csaki (eds.), Budapest, 267-281.

Andersen, T., T. Bollerslev and S. Lange (1999). Forecasting Financial Market Volatility: Sample Frequency vis-à-vis Forecast Horizon. Journal of Empirical Finance, 6, 457-477.

Andersen, T., Bollerslev, T., Christoffersen, P. and Diebold, F.X. (2006). Volatility and Correlation Forecasting. In (eds.) Elliott, G. Granger, C.W.J. and Timmermann, A. Handbook of Economic Forecasting, North Holland Press, Amsterdam.

Baillie, R.T., Bollerslev, T. and Mikkelsen, H.O. (1996). Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 74, 3-30.

Barndorff-Nielsen O.E. and Shephard, N. (2004). Power and bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics, 2, 1-48.

Barndorff-Nielsen, O.E. and Shephard, N. (2005). How Accurate is the Asymptotic Approximation to the Distribution of Realised Volatility? In (eds.) Andrews, D., Powell, J., Ruud, P., and Stock, J., Identification and Inference for Econometric Models. Cambridge University Press, Cambridge.

Barunik, J., Krehlik, T. and Vacha, L. (2016). Modeling and forecasting exchange rate volatility in time-frequency domain. European Journal of Operational Research, 251, 329–340.

Box, G.E.P. and Tiao, G.C. (1973). Bayesian Inference in Statistical Analysis. Addison-Wesley, Reading, Mass.

Chiriac, R. and Voev, V. (2011). Modelling and Forecasting Multivariate Realized Volatility, Journal of Econometrics, 26(6), 922-947.

Choobineh, F. and Branting, D. (1986). A Simple Approximation for Semivariance. European Journal of Operational Research, 27, 364–370.

Christensen K. and Podolskij, M. (2007). Realized range-based estimation of integrated variance. Journal of Econometrics, 141, 323-349.

Corsi, F., Mittnik, S., Pigorsch, C. and Pigorsch, U. (2008). The Volatility of Realised Volatility. Econometric Reviews, 27(1-3), 46-78.

Degiannakis, S. and Floros, C. (2015). Modelling and Forecasting High Frequency Financial Data, Palgrave - MacMillan Ltd., Hampshire.

Degiannakis, S. and Floros, C. (2016). Intra-Day Realized Volatility for European and USA Stock Indices, Global Finance Journal, 29, 24-41.

Degiannakis, S. and Livada, A. (2016). Evaluation of Realized Volatility Predictions from Models with Leptokurtically and Asymmetrically Distributed Forecast Errors, Journal of Applied Statistics, 43(5), 871-892.

Degiannakis, S. and Xekalaki, E. (2005). Predictability and Model Selection in the Context of ARCH Models. Journal of Applied Stochastic Models in Business and Industry, 21, 55-82.

Engle, R.F., C.H. Hong, A. Kane and J. Noh (1993). Arbitrage valuation of variance forecasts with simulated options. Advances in Futures and Options Research, 6, 393-415.

Fernandez, C. and Steel, M. (1998). On Bayesian Modeling of Fat Tails and Skewness. Journal of the American Statistical Association, 93, 359-371.

Granger C.W.J. and M.H. Pesaran (2000). Economic and Statistical Measures of Forecasting Accuracy. Journal of Forecasting, 19, 537-560.

Grootveld H. and Hallerbach, W. (1999). Variance vs downside risk: Is there really that much difference? European Journal of Operational Research, 114, 304–319.

Hansen, P.R. and Lunde, A. (2005). A Realized Variance for the Whole Day Based on Intermittent High-Frequency Data. Journal of Financial Econometrics, 3(4), 525-554.

Hansen, P.R. and Lunde, A. (2006). Realized Variance and Market Microstructure Noise. Journal of Business and Economic Statistics, 24(2), 127-161.

Hendry D.F. and M.P. Clements (2001). Economic Forecasting: Some Lessons from Recent Research. European Central Bank, Working Paper Series, 82.

Heynen, R. and H. Kat (1994). Volatility Prediction: A Comparison of the Stochastic Volatility, Garch(1,1), and Egarch(1,1) Models. Journal of Derivatives, 94, 50-65.

Kibble, W.F. (1941). A Two Variate Gamma Type Distribution. Sankhya, 5, 137-150.

Krishnamoorthy, A.S. and Parthasarathy, M. (1951). A Multivariate Gamma - Type Distribution. Annals of Mathematical Statistics, 22, 4, 549-557.

Kullback, S. and Leibler, R.A. (1951). On Information and Sufficiency. Annals of Mathematical Statistics, 22, 79-86.

Müller, U.A., Dacorogna, M.M., Davé, R.D., Olsen, R.B., Pictet, O.V. and VonWeizsäcker, J.E. (1997). Volatilities of Different Time Resolutions – Analyzing the Dynamics of Market Components. Journal of Empirical Finance, 4, 213-239.

Pagan, A.R. and G.W. Schwert (1990). Alternative Models for Conditional Stock Volatility. Journal of Econometrics, 45, 267-290.

Patton, A.J. (2011). Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics, 160(1), 246-256.

Prokopczuk, M., Symeonidis, L., and Wese Simen, C. (2016). Do Jumps Matter for Volatility Forecasting? Evidence from Energy Markets. Journal of Futures Markets, forthcoming.

Schwarz, G. (1978). Estimating the Dimension of a Model. Annals of Statistics, 6, 461-464.

Sevi, B. (2014). Forecasting the Volatility of Crude Oil Futures using Intraday Data. European Journal of Operational Research, 235, 643-659.

Shibata, R. (1980). Asymptotically Efficient Selection of the Order of the Model for Estimating Parameters of a Linear Process. Annals of Statistics, 8, 147-164.

West, K. D., H. J. Edison, and D. Cho, (1993). A Utility Based Comparison of Some Models for Exchange Rate Volatility. Journal of International Economics, 35, 23-45.

Xekalaki, E. and Degiannakis, S. (2005). Evaluating Volatility Forecasts in Option Pricing in the Context of a Simulated Options Market. Computational Statistics and Data Analysis, 49(2), 611-629.

Xekalaki, E. and Degiannakis, S. (2010). ARCH Models for Financial Applications. John Wiley & Sons Ltd., New York.

Zhang, L., Mykland, P.A., Aït-Sahalia, Y. (2005). A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association, 100, 1394-1411.