The Korean Journal of Applied Statistics (응용통계연구)

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

함수적 변동성 fGARCH(1, 1)모형을 통한 초고빈도 시계열 변동성

  • 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

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.

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.

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References

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