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).

References

  1. Bollerslev T (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  2. Choi MS, Park JA, and Hwang SY (2012). Asymmetric GARCH processes featuring both threshold effect and bilinear structure, Statistics & Probability Letters, 82, 419-426. https://doi.org/10.1016/j.spl.2011.11.023
  3. Choi SW, Yoon JE, Lee SD, and Hwang SY (2021). Asymmetric and non-stationary GARCH(1, 1) models: Parametric bootstrap to evaluate forecasting performance, Korean Journal of Applied Statistics, 34, 611-622. https://doi.org/10.5351/KJAS.2021.34.4.611
  4. Engle RF (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1008. https://doi.org/10.2307/1912773
  5. Engle RF and Ng VK (1993). Measuring and testing the impact of news on volatility, Journal of Finance, 48, 1749-1778. https://doi.org/10.1111/j.1540-6261.1993.tb05127.x
  6. Kim DR and Hwang SY (2020). Forecasting evaluation via parametric bootstrap for threshold-INARCH models, Communications for Statistical Applications and Methods, 27, 177-187. https://doi.org/10.29220/CSAM.2020.27.2.177
  7. Lee HR and Hwang SY (2022). Multiple-threshold asymmetric volatility models for financial time series, Korean Journal of Applied Statistics, 35, 347-356.
  8. Miguel JA and Olave P (1999). Bootstrapping forecast intervals in ARCH models, TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 8, 345-346. https://doi.org/10.1007/BF02595875
  9. Tsay RS (2010). Analysis of Financial Time Series (3rd ed), Wiley, New York.
  10. Yoon JE, Lee JW, and Hwang SY (2014). News impact curves of volatility for asymmetric GARCH via LASSO, Korean Journal of Applied Statistics, 27, 159-168. https://doi.org/10.5351/KJAS.2014.27.1.159