The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Asymptotic properties of monitoring procedure for parameter change in heteroscedastic time series models

이분산 시계열 모형에서 모수의 변화에 대한 모니터링 절차의 점근 성질

  • Kim, Soo Taek (Department of Information and Statistics, Gyeongsang National University) ;
  • Oh, Hae June (Department of Information and Statistics, Gyeongsang National University)
  • 김수택 (경상대학교 정보통계학과) ;
  • 오해준 (경상대학교 정보통계학과)
  • Received : 2020.07.09
  • Accepted : 2020.07.15
  • Published : 2020.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

We investigate a monitoring procedure for the early detection of parameter changes in location-scale time series models. We introduce a detector for monitoring procedure based on modified residual cumulative sum (CUSUM). The asymptotic properties of the monitoring procedure are established under the null and alternative hypotheses. Simulation results and data analysis are also provided for illustration.

본 논문은 이분산성을 갖는 위치-척도 시계열 모형에서 모수의 변화에 대한 모니터링 절차를 연구한다. 모니터링 절차에서 수정된 잔차의 누적합을 이용한 탐지기를 소개하고 귀무가설과 대립가설 하에서 각각 모니터링 절차에 대한 점근적 성질을 규명한다. 그리고 모의실험과 사례 분석을 통하여 제안한 모니터링 방법의 성능이 우수함을 확인한다.

Keywords

References

  1. Aue, A., Dienes, C., Fremdt, S., and Steinebach, J. (2015). Reaction times of monitoring schemes for ARMA time series, Bernoulli, 21, 1238-1259. https://doi.org/10.3150/14-BEJ604
  2. Bardet, J. M. and Kengne, W. (2014). Monitoring procedure for parameter change in causal time series, Journal of Multivariate Analysis, 125, 204-221. https://doi.org/10.1016/j.jmva.2013.12.004
  3. Berkes, I., Gombay, E., Horvath, L., and Kokoszka, P. (2004a). Sequential change-point detection in GARCH(p, q) models, Econometric Theory, 20, 1140-1167. https://doi.org/10.1017/S0266466604206041
  4. Berkes, I., Horvath, L., and Kokoszka, P. (2004b). Testing for parameter constancy in GARCH(p, q) models, Statistics & Probability Letters, 70, 263-273. https://doi.org/10.1016/j.spl.2004.10.010
  5. Chu, C. S. J., Stinchcombe, M., and White, H. (1996). Monitoring structural change, Econometrica:Journal of the Econometric Society, 1045-1065.
  6. Csorgo, M. and Revesz, P. (2014). Strong Approximations in Probability and Statistics, Academic Press, New York.
  7. Dienes, C. and Aue, A. (2014). On-line monitoring of pollution concentrations with autoregressive moving average time series, Journal of Time Series Analysis, 35, 239-261. https://doi.org/10.1111/jtsa.12062
  8. Francq, C. and Zakoian, J. M. (2019). GARCH Models: Structure, Statistical Inference and Financial Applications (2nd ed), John Wiley & Sons, Hoboken.
  9. Gombay, E. (2008). Change detection in autoregressive time series, Journal of Multivariate Analysis, 99, 451-464. https://doi.org/10.1016/j.jmva.2007.01.003
  10. Gombay, E. and Serban, D. (2009). Monitoring parameter change in AR(p) time series models, Journal of Multivariate Analysis, 100, 715-725. https://doi.org/10.1016/j.jmva.2008.08.005
  11. Horvath, L., Huskova, M., Kokoszka, P., and Steinebach, J. (2004). Monitoring changes in linear models, Journal of Statistical Planning and Inference, 126, 225-251. https://doi.org/10.1016/j.jspi.2003.07.014
  12. Kengne, W. (2015). Sequential change-point detection in Poisson autoregressive models, Journal de la Socete Francaise de Statistique, 156, 98-112.
  13. Kim, S., Cho, S., and Lee, S. (2000). On the CUSUM test for parameter changes in GARCH(1, 1) models, Communications in Statistics-Theory and Methods, 29, 445-462. https://doi.org/10.1080/03610920008832494
  14. Kirch, C. and Kamgaing, J. T. (2012). Testing for parameter stability in nonlinear autoregressive models, Journal of Time Series Analysis, 33, 365-385. https://doi.org/10.1111/j.1467-9892.2011.00764.x
  15. Lee, S. and Song, J. (2008). Test for parameter change in ARMA models with GARCH innovations, Statistics & Probability Letters, 78, 1990-1998. https://doi.org/10.1016/j.spl.2008.01.068
  16. Lee, S., Ha, J., Na, O., and Na, S. (2003). The CUSUM test for parameter change in time series models, Scandinavian Journal of Statistics, 30, 781-796. https://doi.org/10.1111/1467-9469.00364
  17. Lee, S., Tokutsu, Y., and Maekawa, K. (2004). The CUSUM test for parameter change in regression models with ARCH errors, Journal of the Japan Statistical Society, 34, 173-188. https://doi.org/10.14490/jjss.34.173
  18. Leisch, F., Hornik, K., and Kuan, C. M. (2000). Monitoring structural changes with the generalized fluctuation test, Econometric Theory, 16, 835-854. https://doi.org/10.1017/S0266466600166022
  19. Li, F., Tian, Z., and Qi, P. (2015). Structural change monitoring for random coefficient autoregressive time series, Communications in Statistics-Simulation and Computation, 44, 996-1009. https://doi.org/10.1080/03610918.2013.800205
  20. Na, O., Lee, Y., and Lee, S. (2011). Monitoring parameter change in time series models, Statistical Methods & Applications, 20, 171-199. https://doi.org/10.1007/s10260-011-0162-3
  21. Oh, H. and Lee, S. (2018). On score vector-and residual-based CUSUM tests in ARMA-GARCH models, Statistical Methods & Applications, 27, 385-406. https://doi.org/10.1007/s10260-017-0408-9
  22. Oh, H. and Lee, S. (2019a). Modified residual CUSUM test for location-scale time series models with heteroscedasticity, Annals of the Institute of Statistical Mathematics, 71, 1059-1091. https://doi.org/10.1007/s10463-018-0679-4
  23. Oh, H. and Lee, S. (2019b). Parameter change test for location-scale time series models with heteroscedasticity based on bootstrap, Applied Stochastic Models in Business and Industry, 35, 1322-1343. https://doi.org/10.1002/asmb.2482
  24. Page, E. S. (1955). A test for a change in a parameter occurring at an unknown point, Biometrika, 42, 523-527. https://doi.org/10.1093/biomet/42.3-4.523
  25. Song, J. and Kang, J. (2018). Parameter change tests for ARMA-GARCH models, Computational Statistics & Data Analysis, 121, 41-56. https://doi.org/10.1016/j.csda.2017.12.002
  26. Song, J. and Kang, J. (2020). Sequential change point detection in ARMA-GARCH models, Journal of Statistical Computation and Simulation, 90, 1520-1538. https://doi.org/10.1080/00949655.2020.1734807
  27. Zeileis, A., Leisch, F., Kleiber, C., and Hornik, K. (2005). Monitoring structural change in dynamic econometric models, Journal of Applied Econometrics, 20, 99-121. https://doi.org/10.1002/jae.776