원점이 이동한 비대칭-변동성 모형의 제안 및 응용
Asymmetric volatility models with non-zero origin shifted from zero : Proposal and application
이예진a, 황선영a, 이성덕1,b
Ye Jin Leea, Sun Young Hwanga, Sung Duck Lee1,b
a숙명여자대학교 통계학과; b충북대학교 정보통계학과
aDepartment of Statistics, Sookmyung Women’s University;
bDepartment of Information and Statistics, Chungbuk National University
bDepartment of Information and Statistics, Chungbuk National University
1 Department of Information and Statistics, Chungbuk National University, Cheongju, Chungbuk 28644, Korea. E-mail: sdlee@chungbuk.ac.kr
This work was partially supported by a grant from the National Research Foundation of Korea (NRF-2021R1F1A1047952).
This work was partially supported by a grant from the National Research Foundation of Korea (NRF-2021R1F1A1047952).
Received August 15, 2023; Revised September 11, 2023; Accepted September 12, 2023.
- Abstract
- 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.
- 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.
- 주요어 : 비대칭 변동성, 원점 이동한 변동성, 모수적 붓스트랩
- Keywords : asymmetric volatility, parametric bootstrap, volatility with non-zero origin
- References
- Bollerslev T (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327.
- Choi MS, Park JA, and Hwang SY (2012). Asymmetric GARCH processes featuring both threshold e ect and bilinear structure, Statistics & Probability Letters, 82, 419-426.
- 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.
- Engle RF (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1008.
- Engle RF and Ng VK (1993). Measuring and testing the impact of news on volatility, Journal of Finance, 48, 1749-1778.
- Kim DR and Hwang SY (2020). Forecasting evaluation via parametric bootstrap for threshold-INARCH models, Communications for Statistical Applications and Methods, 27, 177-187.
- Lee HR and Hwang SY (2022). Multiple-threshold asymmetric volatility models for financial time series, Korean Journal of Applied Statistics, 35, 347-356.
- 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.
- Tsay RS (2010). Analysis of Financial Time Series (3rd ed), Wiley, New York.
- 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.
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