The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Asymmetric volatility models with non-zero origin shifted from zero : Proposal and application

원점이 이동한 비대칭-변동성 모형의 제안 및 응용

  • Ye Jin Lee (Department of Statistics, Sookmyung Women's University) ;
  • Sun Young Hwang (Department of Statistics, Sookmyung Women's University) ;
  • Sung Duck Lee (Department of Information and Statistics, Chungbuk National University)
  • 이예진 (숙명여자대학교 통계학과) ;
  • 황선영 (숙명여자대학교 통계학과) ;
  • 이성덕 (충북대학교 정보통계학과)
  • Received : 2023.08.15
  • Accepted : 2023.09.12
  • Published : 2023.12.31
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Abstract

Volatility of a time series is defined as the conditional variance on the past information. In particular, for financial time series, volatility is regarded as a time-varying measure of risk for the financial series. To capture the intrinsic asymmetry in the risk of financial series, various asymmetric volatility processes including threshold-ARCH (TARCH, for short) have been proposed in the literature (see, for instance, Choi et al., 2012). This paper proposes a volatility function featuring non-zero origin in which the origin of the volatility is shifted from the zero and therefore the resulting volatility function is certainly asymmetric around zero and achieves the minimum at a non-zero (rather than zero) point. To validate the proposed volatility function, we analyze the Korea stock prices index (KOSPI) time series during the Covid-19 pandemic period for which origin shift to the left of the zero in volatility is shown to be apparent using the minimum AIC as well as via parametric bootstrap verification.

본 논문에서는 비대칭 변동성을 다루고 있다. 대표적인 비대칭 모형인 분계점-ARCH에서 원점이 영(zero)에서 이동한 모형을 제안하고 있다. 제안된 모형은 변동성의 최소값이 비-영(non-zero)에서 생기는 특수한 구조의 비대칭 모형이며 AIC 등의 모형선택기준과 더불어 모수적-붓스트랩을 통한 예측분포를 이용하여 원점으로부터의 이동량을 결정할 수 있다. 팬데믹 기간의 국내 종합주가지수(KOSPI) 자료 분석을 통해 모형의 응용 절차를 예시하였다.

Keywords

Acknowledgement

본 연구는 한국연구재단의 지원을 받았습니다 (NRF-2021R1F1A1047952).

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