Simulated Evidence on the Distribution of the Standardized One-Step-Ahead Prediction Errors in ARCH Processes

Degiannakis, Stavros and Xekalaki, Evdokia (2007): Simulated Evidence on the Distribution of the Standardized One-Step-Ahead Prediction Errors in ARCH Processes. Published in: Applied Financial Economics Letters No. 3 (2007): pp. 31-37.

Abstract

In statistical modeling contexts, the use of one-step-ahead prediction errors for testing hypotheses on the forecasting ability of an assumed model has been widely considered. Quite often, the testing procedure requires independence in a sequence of recursive standardized prediction errors, which cannot always be readily deduced particularly in the case of econometric modeling. In this paper, the results of a series of Monte Carlo simulations reveal that independence can be assumed to hold.

• Item Type: MPRA Paper
• Language: English
• Keywords: ARCH models, Monte Carlo Simulation, One-step-ahead Prediction Errors, Predictability, Standardized Prediction Error Criterion
• Subjects: 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 > C4 - Econometric and Statistical Methods: Special Topics > C40 - General; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods ; Simulation Methods

References

Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics, 31, 307-327.

Bollerslev, T., R.F., Engle and D., Nelson (1994). ARCH Models. Ch.49 in R. F. Engle and D. L. McFadden eds. Handbook of Econometrics, IV Elsevier.

Brock, W., D., Dechert, J., Sheinkman and B., LeBaron (1996). A Test for Independence Based on the Correlation Dimension, Econometric Reviews, 15(3), 197-235.

Degiannakis, S. and E., Xekalaki, (2001). Using a Prediction Error Criterion for Model Selection in Forecasting Option Prices, Athens University of Economics and Business, Department of Statistics, Technical Report, 131.

Degiannakis, S. and E., Xekalaki (2004). Autoregressive Conditional Heteroscedasticity Models: A Review. Quality Technology and Quantitative Management, 1(2), 271-324.

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

Degiannakis, S. and E., Xekalaki (2005b). Assessing the Performance of a Prediction Error Criterion Model Selection Algorithm in the Context of ARCH Models, Applied Financial Economics, forthcoming.

Degiannakis, S. and E., Xekalaki (2005c). On the Independence of the Standardized One-Step-Ahead Prediction Errors in ARCH Models. Paper presented at the 7th Hellenic-European Conference on Computer Mathematics and its Applications, Athens, Greece.

Ding, Z. and C.W.J., Granger (1996). Modeling Volatility Persistence of Speculative Returns: A New Approach. Journal of Econometrics, 73, 185-215.

Engle, R.F. and C., Mustafa (1992). Implied ARCH models from options prices, Journal of Econometrics, 52, 289-311.

Glosten, L.R., R., Jagannathan and D.E., Runkle (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48, 1779-1801.

He, C. and T., Teräsvirta (1999). Properties of Moments of a Family of GARCH Processes. Journal of Econometrics, 92, 173-192.

Karanasos, M. (1999). The Second Moment and the Autoregressive Function of the Squared Errors of the GARCH Model. Journal of Econometrics, 90, 63-76.

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

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