Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

An Empirical Study on Explosive Volatility Test with Possibly Nonstationary GARCH(1, 1) Models

  • Lee, Sangyeol (Department of Statistics, Seoul National University) ;
  • Noh, Jungsik (Department of Statistics, Seoul National University)
  • Received : 2013.03.26
  • Accepted : 2013.05.15
  • Published : 2013.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we implement an empirical study to test whether the time series of daily returns in stock and Won/USD exchange markets is strictly stationary or explosive. The results indicate that only a few series show nonstationary volatility when dramatic events erupted; in addition, this nonstationary behavior occurs more often in the Won/USD exchange market than in the stock market.

Keywords

References

  1. Berkes, I., Horvath, L. and Kokoszka, P. (2003). GARCH processes: Structure and estimation, Bernoulli, 9, 201-227. https://doi.org/10.3150/bj/1068128975
  2. Billingsley, P. (1995). Probability and Measure, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons Inc., New York, 3rd edn, A Wiley-Interscience Publication.
  3. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  4. Bougerol, P. and Picard, N. (1992). Stationarity of GARCH processes and of some nonnegative time series, Journal of Econometrics, 52, 115-127. https://doi.org/10.1016/0304-4076(92)90067-2
  5. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007. https://doi.org/10.2307/1912773
  6. Francq, C. and Zakoian, J.-M. (2004). Maximum likelihood estimation of pure GARCH and ARMAGARCH processes, Bernoulli, 10, 605-637. https://doi.org/10.3150/bj/1093265632
  7. Francq, C. and Zakoian, J.-M. (2012). Strict stationarity testing and estimation of explosive and stationary generalized autoregressive conditional heteroscedasticity models, Econometrica, 80, 821-861. https://doi.org/10.3982/ECTA9405
  8. Jensen, S. T. and Rahbek, A. (2004). Asymptotic inference for nonstationary GARCH, Econometric Theory, 20, 1203-1226.
  9. Kingman, J. F. C. (1973). Subadditive ergodic theory, The Annals of Probability, 1, 883-899. https://doi.org/10.1214/aop/1176996798
  10. Lee, S.-W. and Hansen, B. E. (1994). Asymptotic theory for the GARCH(1, 1) quasi-maximum likelihood estimator, Econometric Theory, 10, 29-52. https://doi.org/10.1017/S0266466600008215
  11. Lee, S. and Lee, T. (2012). Inference for Box-Cox transformed threshold garch models with nuisance parameters, Scandinavian Journal of Statistics, 39, 568-589. https://doi.org/10.1111/j.1467-9469.2012.00805.x
  12. Li, W. K., Ling, S. and McAleer, M. (2002). Recent theoretical results for time series models with GARCH errors, Journal of Economic Surveys, 16, 245-269. https://doi.org/10.1111/1467-6419.00169
  13. Lumsdaine, R. L. (1996). Consistency and asymptotic normality of the quasi-maximum likelihood estimator in IGARCH(1, 1) and covariance stationary GARCH(1, 1) models, Econometrica, 64, 575-596. https://doi.org/10.2307/2171862
  14. Medeiros, M. C. and Veiga, A. (2009). Modeling multiple regimes in financial volatility with a flexible coefficient GARCH(1,1) model, Econometric Theory, 25, 117-161. https://doi.org/10.1017/S026646660809004X
  15. Nelson, D. B. (1990). Stationarity and persistence in the GARCH(1, 1) model, Econometric Theory, 6, 318-334. https://doi.org/10.1017/S0266466600005296
  16. Pantula, S. G. (1988). Estimation of autoregressive models with ARCH errors, Sankhya B, 50, 119-138.
  17. Straumann, D. and Mikosch, T. (2006). Quasi-maximum-likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equations approach, The Annals of Statistics, 34, 2449-2495. https://doi.org/10.1214/009053606000000803
  18. Weiss, A. A. (1986). Asymptotic theory for ARCH models: Estimation and testing, Econometric Theory, 2, 107-131. https://doi.org/10.1017/S0266466600011397

Cited by

  1. Skewness of Gaussian Mixture Absolute Value GARCH(1, 1) Model vol.20, pp.5, 2013, https://doi.org/10.5351/CSAM.2013.20.5.395
  2. Exploratory Data Analysis for Korean Stock Data with Recurrence Plots vol.26, pp.5, 2013, https://doi.org/10.5351/KJAS.2013.26.5.807
  3. A generalized regime-switching integer-valued GARCH(1, 1) model and its volatility forecasting vol.25, pp.1, 2018, https://doi.org/10.29220/CSAM.2018.25.1.029