The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Numerical Study on CUSUM Test for Volatility Shifts Against Long-Range Dependence

변동성 변화와 장기억성을 구분하는 CUSUM 검정통계량에 대한 실증분석

  • Lee, Youngsun (Department of statistics, Hankuk University of Foreign Studies) ;
  • Lee, Taewook (Department of statistics, Hankuk University of Foreign Studies)
  • 이영선 (한국외국어대학교 통계학과) ;
  • 이태욱 (한국외국어대학교 통계학과)
  • Received : 2013.12.31
  • Accepted : 2014.03.14
  • Published : 2014.04.30
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Abstract

Persistence is one of the typical characteristics appearing in the volatility of financial time series. According to the recent researches, the volatility persistence may be due to either volatility shifts or long-range dependence. In this paper, we consider residual-based CUSUM tests to distinguish volatility persistence, long-range dependence and volatility shifts in GARCH models. It is observed that this test procedure achieve reasonable powers without a size distortion. Moreover, we employ AIC and BIC criteria to estimate the change points and the number of change points in volatility. We demonstrate the superiority of residual-based CUSUM tests on various Monte Carlo simulations and empirical data analysis.

금융시계열 자료의 변동성에 나타나는 대표적인 현상 중에 지속성(persistence)이 있는데, 이를 설명하기 위하여 IGARCH 모형이 주로 사용된다. 최근에 변동성의 지속성은 변동성 변화와 장기억성에 기인한다는 사실이 많은 연구 결과에서 발표되고 있을 뿐만 아니라 장기억성은 변동성 변화로, 변동성 변화는 장기억성으로 보이게 되는 현상이 빈번히 나타난다. 따라서 본 논문에서는 변동성의 지속성, 장기억성 및 변동성 변화를 구분하는 통계적인 방법론을 고려하였다. 이를 위해 GARCH 모형 잔차를 기반으로 하는 CUSUM 통계량을 도입하여, size 왜곡(distortion) 현상을 해결할 뿐만 아니라 우수한 검정력을 얻을 수 있음을 입증하였다. 한편 변동성 변화가 존재하는 경우 변화점 추정이 중요해 지는데, 이를 위해 GARCH 모형을 기반으로 한 AIC 방법과 BIC 방법을 비교하였다. 다양한 모의실험과 실증자료를 분석하여 우리가 제안하는 잔차 기반의 CUSUM 통계량의 우수성을 입증하였다.

Keywords

Acknowledgement

Supported by : 한국연구재단

References

  1. Andrews, D. (1991). Heteroscedasticity and Autocorrelation Consistent Covariance Matrix Estimation, Econometrica, 59, 817-858. https://doi.org/10.2307/2938229
  2. Baek, C. and Pipiras, V. (2012). Statistical tests for a single change in mean against long-range dependence, Journal of Time Series Analysis, 33, 131-151. https://doi.org/10.1111/j.1467-9892.2011.00747.x
  3. Baillie, R. T., Bollersleve, T. and Mikkelsen, H. O. (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 74, 3-30. https://doi.org/10.1016/S0304-4076(95)01749-6
  4. Berkes, I., Horvath, L. and Kokoszka, P. (2003). GARCH processes: structure and estimation, Bernoulli, 9, 201-227. https://doi.org/10.3150/bj/1068128975
  5. Berkes, I., Horvath, L., Kokoszka, P. and Shao, Q.-M. (2006). On discriminating between long-range dependence and changes in mean. Annals of Statistics 34, 1140-1165. https://doi.org/10.1214/009053606000000254
  6. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  7. Diebold, F. X. and Inoue, A. (2001). Long memory and regime switching, Journal of Econometrics, 105, 131-159. https://doi.org/10.1016/S0304-4076(01)00073-2
  8. Ding, Z., Granger, C. W. J. and Engle, R. F. (1993). A long memory property of stock market returns and a new model, Journal of Empirical Finance, 1, 83-106. https://doi.org/10.1016/0927-5398(93)90006-D
  9. 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
  10. Engle, R. F. and Bollerslev, T. (1986). Modelling the persistence of conditional variances, Econometric Reviews, 5, 1-50. https://doi.org/10.1080/07474938608800095
  11. Francq, C. and Zakoan, J. (2004). Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes, Bernoulli, 10, 605-637. https://doi.org/10.3150/bj/1093265632
  12. Hillebrand, E. (2005). Neglecting parameter changes in GARCH models, Journal of Econometrics, 129, 121-138. https://doi.org/10.1016/j.jeconom.2004.09.005
  13. Klemes, V. (1974). The Hurst phenomenon: a puzzle?, Water Resources Research, 10, 675-688. https://doi.org/10.1029/WR010i004p00675
  14. Kulperger, R. and Yu, H. (2005). High moment partial sum processes of residuals in GARCH models and their applications, The Annals of Statistics, 33, 2395-2422. https://doi.org/10.1214/009053605000000534
  15. Lee, T., Kim, M. and Beak, C. (2014). Tests for volatility shifts in GARCH models against long-range dependence, submitted for publication.
  16. Mikosch, T. and Starica, C. (2004). Nonstationarities in financial time series, the long-range dependence, and the IGARCH effects, The Review of Economics and Statistics, 86, 378-390. https://doi.org/10.1162/003465304323023886
  17. Pooter, M. D. and Dijk, D. V. (2004). Testing for changes in volatility in heteroskedastic time series-a further examination, Econometric Institute Report EI 2004-38, Erasmus University Rotterdam, Econometric Institute.
  18. Teverovsky, V., Taqqu, M. S. and Willinger, W. (1999). A critical look at Lo's modified R/S statistic, Journal of Statistical Planning and Inference, 80, 211-227. https://doi.org/10.1016/S0378-3758(98)00250-X