Stationary Bootstrap Prediction Intervals for GARCH(p,q)

Title & Authors
Stationary Bootstrap Prediction Intervals for GARCH(p,q)
Hwang, Eunju; Shin, Dong Wan;

Abstract
The stationary bootstrap of Politis and Romano (1994) is adopted to develop prediction intervals of returns and volatilities in a generalized autoregressive heteroskedastic (GARCH)(p, q) model. The stationary bootstrap method is applied to generate bootstrap observations of squared returns and residuals, through an ARMA representation of the GARCH model. The stationary bootstrap estimators of unknown parameters are defined and used to calculate the stationary bootstrap samples of volatilities. Estimates of future values of returns and volatilities in the GARCH process and the bootstrap prediction intervals are constructed based on the stationary bootstrap; in addition, asymptotic validities are also shown.
Keywords
GARCH model;stationary bootstrap;prediction;asymptotics;
Language
English
Cited by
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응용통계연구, 2013. vol.26. 5, pp.807-819
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References
1.
Andersen, T. G. and Bollerslev, T. (1998). Answering the skeptics: yes, standard volatility models do provide accurate forecasts, International Economic Review, 39, 885-905.

2.
Andersen, T. G., Bollerslev, T., Diebold, F. X. and Labys, P. (2001). The distribution of realized exchange rate volatility, Journal of the American Statistical Association, 96, 42-55.

3.
Baillie, R. T. and Bollerslev, T. (1992). Prediction in dynamic models with time-dependent conditional variances, Journal of Econometrics, 52, 91-113.

4.
Bougerol, P. and Picard, N. (1992a). Strict stationarity of generalized autoregressive processes, Annals of Probability, 20, 1714-1730.

5.
Bougerol, P. and Picard, N. (1992b). Stationarity of GARCH processes and of some nonnegative time series, Journal of Econometrics, 52, 115-127.

6.
Chen, B., Gel, Y. R., Balakrishna, N. and Abraham, B. (2011). Computationally efficient bootstrap prediction intervals for returns and volatilities in ARCH and GARCH processes, Journal of Forecasting, 30, 51-71.

7.
Engle, R. F. and Patton, A. J. (2001). What good is a volatility model?, Quantitative Finance, 1, 237-245.

8.
Hwang, E. and Shin, D.W. (2011). Stationary bootstrapping for non-parametric estimator of nonlinear autoregressive model, Journal of Time Series Analysis, 32, 292-303.

9.
Hwang, E. and Shin, D. W. (2012a). Stationary bootstrap for kernel density estimators under $\psi$-weak dependence, Computational Statistics and Data Analysis, 56, 1581-1593.

10.
Hwang, E. and Shin, D. W. (2012b). Strong consistency of the stationary bootstrap under $\psi$-weak dependence, Statistics and Probability Letters, 82, 488-495.

11.
Kavalieris, L., Hannan, E. J. and Salau, M. (2003). Generalized least squares estimation of ARMA models, Journal of Time Series Analysis, 24, 165-172.

12.
Koreisha, S. and Pukkila, T. (1990). A generalized least-squares approach for estimation of autoregressive moving-average models, Journal of Time Series Analysis, 11, 139-151.

13.
Lahiri, S. N. (1999). On second-order properties of the stationary bootstrap method for studentized statistics, In Asymptotic, Nonparametrics, and Time Series. (Eds. Ghosh, S.), Marcel Dekker, New York, 683-711.

14.
Miguel, J. A. and Olave, P. (1999). Bootstrapping forecast intervals in ARCH models, Test, 8, 345-364.

15.
Nordman, D. J. (2009). A note on the stationary bootstrap's variance, Annals of Statistics, 37, 359-370.

16.
Paparoditis, E. and Politis, D. N. (2005). Bootstrapping unit root tests for autoregressive time series, Journal of the American Statistical Association, 100, 545-553.

17.
Parker, C., Paparoditis, E. and Politis, D. N. (2006). Unit root testing via the stationary bootstrap, Journal of Econometrics, 133, 601-638.

18.
Pascual, L., Romo, J. and Ruiz, E. (2006). Bootstrap prediction for returns and volatilities in GARCH models, Computational Statistics and Data Analysis, 50, 2293-2312.

19.
Politis, D. N. and Romano, J. P. (1994). The stationary bootstrap, Journal of the American Statistical Association, 89, 1303-1313.

20.
Reeves, J. J. (2005). Bootstrap prediction intervals for ARCH models, Internal Journal of Forecasting, 21, 237-248.

21.
Swensen, A. R. (2003). Bootstrapping unit root tests for integrated processes, Journal of Time Series Analysis, 24, 99-126.

22.
Thombs, L. A. and Schucany,W. R. (1990). Bootstrap prediction intervals for autoregression, Journal of the American Statistical Association, 95, 486-492.