The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Comparison of a Class of Nonlinear Time Series models (GARCH, IGARCH, EGARCH)

이분산성 시계열 모형(GARCH, IGARCH, EGARCH)들의 성능 비교

  • Kim S.Y. (Department of Statistics, Chung-Ang University) ;
  • Lee Y.H. (Department of Statistics, Chung-Ang University)
  • Published : 2006.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we analyse the volatilities in financial data such as stock prices and exchange rates in term of a class of nonlinear time series models. We compare the performance of Generalized Autoregressive Conditional Heteroscadastic(GARCH) , Integrated GARCH(IGARCH), Exponential GARCH(EGARCH) models by KOSPI (Korean stock Prices Index) data. The estimation for the parameters in the models was carried out by the ML methods.

최근 들어 시계열 자료 분석에서 관측된 각 시점에서의 관측치의 분산을 서로 다른 분산(조건부 이분산성)을 따른다고 가정하고, 이를 분석하는 모형(ARCH, GARCH, EGARCH, IGARCH 등)들이 옵션 가격 분석이나 환율 변화 등 경제적 시계열 자료의 예측 모형을 위하여 활발히 연구되고 있다. 본 논문에서는 한국의 KOSPI 데이터 (1999년 1월 4일 $\sim$ 2003년 12월 30일, 총 1227일)를 바탕으로 조건부 우도함수 모수 추정 방법을 이용한 GARCH(1,1), IGARCH(1,1), EGARCH(1,1) 모형에 KOSPI 자료를 적합 시켜 각 모형들의 성능을 비교하여 보았다.

Keywords

References

  1. Awartani, B. M. A. and Corradi, V. (2005). Predicting the volatility of the S&P-500 stock index via GARCH models: the role of asymmetries. International Journal of Forecasting, 21, 167-183 https://doi.org/10.1016/j.ijforecast.2004.08.003
  2. Bollerslev, T. (1986). Generalized autoregressive heteroskedasticity. Journal of Econometrics, 31, 307-327 https://doi.org/10.1016/0304-4076(86)90063-1
  3. El BABSIRI, M. and Zakoian, J. M. (2001). Contemporaneous asymmeties in GARCH processes. Journal of Econometrics, 101, 257-294 https://doi.org/10.1016/S0304-4076(00)00084-1
  4. Engle, R. F. (1982). Autoregressive, conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrca, 50. 987-1007 https://doi.org/10.2307/1912773
  5. Engle, F., Lilien, D. V. and Robins, R. P. (1987). Estimating time varying risk premia in the term structure: The ARCH-M model. Econometrica, 55, 391-407 https://doi.org/10.2307/1913242
  6. Franses, P. H. and Van Dijk, D. (1996). Forecasting stock market volatility using(nonlinear) GARCH models. Journal of Rorecasting, 15(3), 229-235 https://doi.org/10.1002/(SICI)1099-131X(199604)15:3<229::AID-FOR620>3.0.CO;2-3
  7. Gonzalez-Rivera, G., Lee, T. H. and Mishra, S. (2004). Does volatility modelling really mattter? A reality check based on option pricing VaR, and utility function. International Journal of Forecasing, 20, 629-645 https://doi.org/10.1016/j.ijforecast.2003.10.003
  8. Hansen, P. R. and Lunde, A. (2005). A forecast comparison of valatility medels:Does anything beat a GARCH(1,1). Journal of Applied Econometrics,(in press)
  9. Nelson D. B. (1991). Conditional heteroskedasticity in asset returns; A new approack. Econometrica, 59, 347-370 https://doi.org/10.2307/2938260
  10. Poon, S. H. and Granger, C. W. J. (2003). Forecasting volatility in financial markets. Journal of Economic Literature, 41, 478-539 https://doi.org/10.1257/002205103765762743
  11. Schwert, G. W. (1990). Stock volatility and crash of 87, Review of Financial Studies, 3, 77-102 https://doi.org/10.1093/rfs/3.1.77
  12. Zakoian, J. M. (1994). Threshold heteroskedastic models. Journal of Economic Dynamics and Control, 18, 931-955 https://doi.org/10.1016/0165-1889(94)90039-6