Communications for Statistical Applications and Methods

  • 제25권1호
  • /
  • Pages.29-42
  • /
  • 2018
  • /
  • 2287-7843(pISSN)
  • /
  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

A generalized regime-switching integer-valued GARCH(1, 1) model and its volatility forecasting

  • Lee, Jiyoung (Department of Applied Statistics, Gachon University) ;
  • Hwang, Eunju (Department of Applied Statistics, Gachon University)
  • 투고 : 2017.07.04
  • 심사 : 2017.12.12
  • 발행 : 2018.01.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We combine the integer-valued GARCH(1, 1) model with a generalized regime-switching model to propose a dynamic count time series model. Our model adopts Markov-chains with time-varying dependent transition probabilities to model dynamic count time series called the generalized regime-switching integer-valued GARCH(1, 1) (GRS-INGARCH(1, 1)) models. We derive a recursive formula of the conditional probability of the regime in the Markov-chain given the past information, in terms of transition probabilities of the Markov-chain and the Poisson parameters of the INGARCH(1, 1) process. In addition, we also study the forecasting of the Poisson parameter as well as the cumulative impulse response function of the model, which is a measure for the persistence of volatility. A Monte-Carlo simulation is conducted to see the performances of volatility forecasting and behaviors of cumulative impulse response coefficients as well as conditional maximum likelihood estimation; consequently, a real data application is given.

키워드

참고문헌

  1. Al-Osh MA and Alzaid AA (1987). First-order integer-valued autoregressive (INAR(1)) process, Journal of Time Series Analysis, 8, 261-275. https://doi.org/10.1111/j.1467-9892.1987.tb00438.x
  2. Alzeid AA and Al-Osh MA (1990). An integer-valued pth-order autoregressive structure (INAR(p)) process, Journal of Applied Probability, 27, 314-324. https://doi.org/10.2307/3214650
  3. Baillie RT, Bollerslev T, and Mikkelsen HO (1996). Fractionally integrated generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 74, 3-30. https://doi.org/10.1016/S0304-4076(95)01749-6
  4. Brandt PT, Williams JT, Fordham BO, and Pollins B (2000). Dynamic modeling for persistent eventcount time series, American Journal of Political Science, 44, 823-843. https://doi.org/10.2307/2669284
  5. Cai J (1994). A Markov model of switching-regime ARCH, Journal of Business and Economic Statistics, 12, 309-316.
  6. Cui Y andWu R (2016). On conditional maximum likelihood estimation for INGARCH(p, q) models, Statistics and Probability Letters, 118, 1-7.
  7. Davis RA, Dunsmuir WTM, and Wang Y (1999). Modeling time series of count data. In S Ghosh (Ed), Asymptotics, Nonparametrics, and Time Series, (pp. 63-114), Marcel Dekker, New York.
  8. Du JG and Li Y (1991). The integer-valued autoregressive (INAR(p)) model, Journal of Time Series Analysis, 12, 129-142. https://doi.org/10.1111/j.1467-9892.1991.tb00073.x
  9. Ferland R, Latour A, and Oraichi D (2006). Integer-valued GARCH processes, Journal of Time Series Analysis, 27, 923-942. https://doi.org/10.1111/j.1467-9892.2006.00496.x
  10. Fokianos K (2011). Some recent progress in count time series, A Journal of Theoretical and Applied Statistics, 45, 49-58.
  11. Fokianos K, Rahbek A, and Tjostheim R (2009). Poisson autoregression, Journal of the American Statistical Association, 104, 1430-1439. https://doi.org/10.1198/jasa.2009.tm08270
  12. Gray SF (1996). Modeling the conditional distribution of interest rates as a regime-switching process, Journal of Financial Economics, 42, 27-62. https://doi.org/10.1016/0304-405X(96)00875-6
  13. Haas M, Mittnik S, and Paolella MS (2004). Mixed normal conditional heteroskedasticity, Journal of Financial Econometrics, 2, 211-250. https://doi.org/10.1093/jjfinec/nbh009
  14. Hamilton JD and Susmel R (1994). Autoregressive conditional heteroskedasticity and changes in regime, Journal of Econometrics, 64, 307-333. https://doi.org/10.1016/0304-4076(94)90067-1
  15. Hong WT and Hwang E (2016). Dynamic behavior of volatility in a nonstationary generalized regimeswitching GARCH model, Statistics and Probability Letters, 115, 36-44. https://doi.org/10.1016/j.spl.2016.04.002
  16. Klaassen F (2002). Improving GARCH volatilities forecasts with regime-switching GARCH, Empirical Economics, 27, 363-394. https://doi.org/10.1007/s001810100100
  17. Lee SY and Noh JS (2013). An empirical study on explosive volatility test with possibly nonstationary GARCH(1, 1) models, Communications for Statistical Applications and Methods, 20, 207-215. https://doi.org/10.5351/CSAM.2013.20.3.207
  18. Marcucci J (2005). Forecasting stock market volatility with regime-switching GARCH models, Studies in Nonlinear Dynamics and Econometrics, 9, 1-55
  19. McKenzie Ed (1988). Some ARMA models for dependent sequences of Poisson counts, Advances in Applied Probability, 20, 822-835.