Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
권호 표지
DOI QR코드

DOI QR Code

Some limiting properties for GARCH(p, q)-X processes

  • Lee, Oesook (Department of Statistics, Ewha Womans University)
  • Received : 2017.03.27
  • Accepted : 2017.05.24
  • Published : 2017.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we propose a modified GARCH(p, q)-X model which is obtained by adding the exogenous variables to the modified GARCH(p, q) process. Some limiting properties are shown under various stationary and nonstationary exogenous processes which are generated by another process independent of the noise process. The proposed model extends the GARCH(1, 1)-X model studied by Han (2015) to various GARCH(p, q)-type models such as GJR GARCH, asymptotic power GARCH and VGARCH combined with exogenous process. In comparison with GARCH(1, 1)-X, we expect that many stylized facts including long memory property of the financial time series can be explained effectively by modified GARCH(p, q) model combined with proper additional covariate.

Keywords

References

  1. Atsmegiorgis, C., Kim, J. and Yoon, S. (2016). The GARCH-GPD in market risks modeling: An empirical exposition on KOSPI. Journal of the Korean data & Information Science Society, 27, 1661-1671. https://doi.org/10.7465/jkdi.2016.27.6.1661
  2. Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31, 307-321. https://doi.org/10.1016/0304-4076(86)90063-1
  3. Brenner, R., Harjes, R. and Kroner, K. (1996). Another look at models of the short-term interest rate. Journal of Financial and Quantitative Analysis, 31, 85-107. https://doi.org/10.2307/2331388
  4. Davidson, J. (2002). Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes. Journal of Econometrics, 105, 243-269.
  5. Davidson, J. and De Jong, R. M. (2000). The functional central limit theorem and weak convergence to stochastic integrals II: Fractionally integrated processes. Econometrics Theory, 16, 643-666. https://doi.org/10.1017/S0266466600165028
  6. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of variance of U.K. inflation. Econometrica, 50, 987-1008. https://doi.org/10.2307/1912773
  7. Engle, R. F. and Patton, A. (2001). What good is a volatility models?. Quantitative Finance, 1, 237-245. https://doi.org/10.1088/1469-7688/1/2/305
  8. Fleming, T., Kirby, C. and Ostdiek, B. (2008). The specification of GARCH models with stochastic covari ates. Journal of Futures Markets, 28, 911-934. https://doi.org/10.1002/fut.20340
  9. Giraitis, L., Leipus, R. and Surgailis, D. (2007). Recent advances in ARCH modelling. In Long Memory in Economics (pp.3-38). Berlin, Springer.
  10. Han, H. (2015). Asymptotic properties of GARCH-X processes. Journal of Financial Econometrics, 13, 188-221. https://doi.org/10.1093/jjfinec/nbt023
  11. Han, H. and Park, J. Y. (2008). Time series properties of ARCH processes with persistent covariates. Journal of Econometrics, 146, 275-292. https://doi.org/10.1016/j.jeconom.2008.08.016
  12. Hwang, S. and Satchell, S. (2005). GARCH model with cross-sectional volatility: GARCH-X models. Applied Financial Economics, 15, 203-216. https://doi.org/10.1080/0960310042000314214
  13. Jeong, S. H. and Lee, T. W. (2017). A numerical study on option pricing based on GARCH models with normal mixture errors. Journal of the Korean data & Information Science Society, 28, 251-260. https://doi.org/10.7465/jkdi.2017.28.2.251
  14. Lee, O. (2014). Functional central limit theorems for augmented GARCH(p,q) and FIGARCH processes. Journal of the Korean Statistical Society, 43, 393-401. https://doi.org/10.1016/j.jkss.2013.12.001
  15. Park, J. (2002). Nonstationary nonlinear heteroscedasticity. Journal of Econometrics, 110, 383-415. https://doi.org/10.1016/S0304-4076(02)00100-8
  16. Park, J. and Phillips, P. (1999). Asymptotics for nonlinear transformations of integrated time series. Econometric Theory, 15, 269-298.
  17. Park, J. and Phillips, P. (2001). Nonlinear regressions with integrated time series. Econometrica, 69, 117-161. https://doi.org/10.1111/1468-0262.00180
  18. Phillips, P. and Solo, V. (1992). Asymptotics for linear processes. The Annals of Statistics, 20, 971-1001. https://doi.org/10.1214/aos/1176348666