응용통계연구 (The Korean Journal of Applied Statistics)

  • 제31권5호
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  • Pages.667-675
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  • 2018
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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함수적 변동성 fGARCH(1, 1)모형을 통한 초고빈도 시계열 변동성

The fGARCH(1, 1) as a functional volatility measure of ultra high frequency time series

  • Yoon, J.E. (Department of Statistics, Sookmyung Women's University) ;
  • Kim, Jong-Min (Statistics Discipline, University of Minnesota-Morris) ;
  • Hwang, S.Y. (Department of Statistics, Sookmyung Women's University)
  • Received : 2018.08.17
  • Accepted : 2018.08.22
  • Published : 2018.10.31
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Abstract

초고빈도(ultra high frequency; UHF)시계열의 함수적 변동성 측정을 위한 최신 기법인 함수적 변동성 functional GARCH : fGARCH(1, 1) 모형을 소개하고 설명하였다. 실증분석을 위해 R-code fGARCH(1, 1) 프로그램을 KOSPI/현대차 초고빈도 수익률 자료에 적합하여 예시하였다.

When a financial time series consists of daily (closing) returns, traditional volatility models such as autoregressive conditional heteroskedasticity (ARCH) and generalized ARCH (GARCH) are useful to figure out daily volatilities. With high frequency returns in a day, one may adopt various multivariate GARCH techniques (MGARCH) (Tsay, Multivariate Time Series Analysis With R and Financial Application, John Wiley, 2014) to obtain intraday volatilities as long as the high frequency is moderate. When it comes to the ultra high frequency (UHF) case (e.g., one minute prices are available everyday), a new model needs to be developed to suit UHF time series in order to figure out continuous time intraday-volatilities. Aue et al. (Journal of Time Series Analysis, 38, 3-21; 2017) proposed functional GARCH (fGARCH) to analyze functional volatilities based on UHF data. This article introduces fGARCH to the readers and illustrates how to estimate fGARCH equations using UHF data of KOSPI and Hyundai motor company.

Keywords

References

  1. Aue, A., Horvath, L., and Pellatt, D. F. (2017). Functional generalized autoregressive conditional heteroskedasticity, Journal of Time Series Analysis, 38, 3-21. https://doi.org/10.1111/jtsa.12192
  2. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  3. Hansen, P. R. and Lunde, A. (2005). A forecast comparison of volatility models: does anything beat a GARCH (1, 1)?, Journal of Applied Econometrics, 20, 873-889. https://doi.org/10.1002/jae.800
  4. Hormann, S., Horvath, L., and Reeder, R. (2013). A functional version of the ARCH model, Econometric Theory, 29, 267-288. https://doi.org/10.1017/S0266466612000345
  5. Jin, M. K., Yoon, J. E., and Hwang, S. Y. (2017). Choice of frequency via principal component in high-frequency multivariate volatility models, The Korean Journal of Applied Statistics, 30, 747-757. https://doi.org/10.5351/KJAS.2017.30.5.747
  6. Kim, J. Y. and Hwang, S. Y. (2018). A threshold-asymmetric realized volatility for high frequency financial time series, The Korean Journal of Applied Statistics, 31, 205-216.
  7. Lee, G. J. and Hwang, S. Y. (2017). Multivariate volatility for high-frequency financial series, The Korean Journal of Applied Statistics, 30, 169-180. https://doi.org/10.5351/KJAS.2017.30.1.169
  8. Li, W. K. (2004). Diagnostic Checks in Time Series, Chapman & Hall/CRC, New York.
  9. Martens, M. (2002). Measuring and forecasting S&P 500 index-futures volatility using high-frequency data, Journal of Futures Markets, 22, 497-518. https://doi.org/10.1002/fut.10016
  10. Tsay, R. S. (2010). Analysis of Financial Time Series (3rd ed), John Wiley & Sons, New York.
  11. Tsay, R. S. (2014). Multivariate Time Series Analysis : With R and Financial Application, John Wiley & Sons, New York.
  12. Yoon, J. E. and Hwang, S. Y. (2015). Volatility computations for financial time series : high frequency and hybrid method, The Korean Journal of Applied Statistics, 28, 1163-1170. https://doi.org/10.5351/KJAS.2015.28.6.1163
  13. Yoon, J. E., Kim, J. M., and Hwang, S. Y. (2017). Functional ARCH (fARCH) for high-frequency time series : illustration, The Korean Journal of Applied Statistics, 30, 983-991.