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비대칭 금융 시계열을 위한 다중 임계점 변동성 모형

Multiple-threshold asymmetric volatility models for financial time series

  • 이효령 (숙명여자대학교 통계학과) ;
  • 황선영 (숙명여자대학교 통계학과)
  • 투고 : 2022.01.06
  • 심사 : 2022.02.02
  • 발행 : 2022.06.30

초록

본 논문에서는 금융 시계열 비대칭 변동성을 모형화하기 위해서 다중 임계점을 가진 비대칭-ARCH 점화식(A-ARCH(1))을 제안하고 있다. 특히 임계점이 두 개인 간단한 모형에 초점을 맞추어 설명하고 있으며 미국 S&P500 자료 분석을 통해 예시하였다. 다양한 A-ARCH(1) 모형의 예측력 비교를 위해 모수적-붓스트랩을 활용하여 예측오차의 평가 및 예측구간의 정확도를 설명하였다.

This article is concerned with asymmetric volatility models for financial time series. A generalization of standard single-threshold volatility model is discussed via multiple-threshold in which we specialize to twothreshold case for ease of presentation. An empirical illustration is made by analyzing S&P500 data from NYSE (New York Stock Exchange). For comparison measures between competing models, parametric bootstrap method is used to generate forecast distributions from which summary statistics of CP (Coverage Probability) and PE (Prediction Error) are obtained. It is demonstrated that our suggestion is useful in the field of asymmetric volatility analysis.

키워드

과제정보

This work was supported by a grant from the National Research Foundation of Korea (NRF-2021R1F1A1047952).

참고문헌

  1. Belisle CJP (1992). Convergence theorems for a class of simulated annealing algorithms, Journal of Applied Probability, 29, 885-895. https://doi.org/10.1017/S002190020004376X
  2. Bollerslev T (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31(3), 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  3. Byrd RH, Lu P, Nocedal J, and Zhu C (1995). A limited memory algorithm for bound constrained optimization, SIAM Journal on Scientific Computing, 16, 1190-1208. https://doi.org/10.1137/0916069
  4. Choi SW, Hwang SY, and Lee SD (2020). Volatility-non-stationary GARCH(1,1) models featuring thresholdasymmetry and power transformation, Korean Journal of Applied Statistics, 33, 713-722. https://doi.org/10.5351/KJAS.2020.36.6.713
  5. 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, 611-621. https://doi.org/10.5351/KJAS.2021.34.4.611
  6. 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
  7. Fletcher R and ReevesCM(1964). Function minimization by conjugate gradients. Computer Journal, 7, 148-154. https://doi.org/10.1093/comjnl/7.2.148
  8. Guerrout E, Ait-Aoudia S, Michelucci D, and Mahiou R (2018). Hidden Markov random field model and Broyden-Fletcher-Goldfarb-Shanno algorithm for brain image segmentation, Journal of Experimental & Theoretical Artificial Intelligence, 30(3), 415-427. https://doi.org/10.1080/0952813x.2017.1409280
  9. Hwang SY, Baek JS, Park JA, and Choi MS (2010). Explosive volatilities for threshold-GARCH processes generated by asymmetric innovations, Statistics & Probability Letters, 80, 26-33. https://doi.org/10.1016/j.spl.2009.09.008
  10. 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
  11. 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, 345-364. https://doi.org/10.1007/BF02595875
  12. Nelder JA and Mead R (1965). A simplex algorithm for function minimization. Computer Journal, 8, 308-313. https://doi.org/10.1093/comjnl/7.4.308
  13. Nocedal J and Wright SJ (1999). Numerical Optimization. Springer.
  14. Rabemananjara R and Zakoian JM (1993). Threshold ARCH models and asymmetries in volatility, Journal of Applied Econometrics, 8, 31-49. https://doi.org/10.1002/jae.3950080104
  15. Tsay RS (2010). Analysis of Financial Time Series, Third Ed, Wiley, New York.
  16. Yoon JE and Hwang SY (2015). Volatility computations for financial time series : high frequency and hybrid method, Korean Journal of Applied Statistics, 28, 1163-1170. https://doi.org/10.5351/KJAS.2015.28.6.1163
  17. 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