응용통계연구 (The Korean Journal of Applied Statistics)

  • 제29권1호
  • /
  • Pages.1-12
  • /
  • 2016
  • /
  • 1225-066X(pISSN)
  • /
  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지
DOI QR코드

DOI QR Code

금융 및 특수시계열 모형의 조망

A recent overview on financial and special time series models

  • 황선영 (숙명여자대학교 통계학과)
  • Hwang, S.Y. (Department of Statistics, Sookmyung Women's University)
  • 투고 : 2016.01.18
  • 심사 : 2016.01.21
  • 발행 : 2016.02.29
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

금융시계열은 일반 시계열과는 차별적으로 stylized facts로 불리는 특징을 가지고 있다. 이 특징들은 급첨 성질, 비정규분포, 변동성 집중 및 비대칭성을 포함한다. 이러한 특징들을 설명하기 위해서는 기존의 선형 ARMA 모형에서 벗어난 특수한 모형이 필요하게 되었다. 본 논문은 변동성 모형인 GARCH 형태의 모형을 중심으로 특수 금융시계열 모형들을 소개하고 연관된 통계적 이슈들에 대해 가능한 최근 연구를 중심으로 폭 넓게 조망하고 있다.

Contrasted with the standard linear ARMA models, financial time series exhibits non-standard features such as fat-tails, non-normality, volatility clustering and asymmetries which are usually referred to as "stylized facts" in financial time series context (Terasvirta, 2009). We are accordingly led to ad hoc models (apart from ARMA) to accommodate stylized facts (Andersen et al., 2009). The paper aims to give a contemporary overview on financial and special time series models based on the recent literature and on the author's publications. Various models are illustrated including asymmetric models, integer valued models, multivariate models and high frequency models. Selected statistical issues on the models are discussed, bringing some perspectives to the future works in this area.

키워드

참고문헌

  1. Andersen, T. G. and Bollerslev, T. (1997). Intraday periodicity and volatility persistence in financial markets, Journal of Empirical Finance, 4, 115-158. https://doi.org/10.1016/S0927-5398(97)00004-2
  2. Andersen, T. G., Davis, R. A., Kreiss, J.-P., and Mikosch, T. (2009). Handbook of Financial Time Series, Springer, Berlin.
  3. Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity, Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-4076(86)90063-1
  4. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994). Time Series Analysis: Forecasting and Control, 3rd Ed., Prentice Hall, New Jersey.
  5. Choi, S. M., Hong, S. Y., Choi, M. S., Park, J. A., Baek, J. S., and Hwang, S. Y. (2009). Analysis of multivariate-GARCH via DCC modeling, Korean Journal of Applied Statistics, 22, 995-1005. https://doi.org/10.5351/KJAS.2009.22.5.995
  6. Chung, S. and Hwang, S. Y. (2016a). A profile Godambe information of power transformations for ARCH time series, to appear in Communications in Statistics-Theory and Methods.
  7. Chung, S. and Hwang, S. Y. (2016b). Stock return volatility based on intraday high frequency data: double-threshold ACD-GARCH Model, to appear in Korean Journal of Applied Statistics.
  8. Connor, G. (1995). Three types of factor models: a comparison of their explanatory power, Financial Analysis Journal, 51, 42-46.
  9. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007. https://doi.org/10.2307/1912773
  10. Engle, R. F. and Ng, V. K. (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
  11. Engle, R. F. and Russell, J. R. (1998). Autoregressive conditional duration: a new model for irregularly spaced transaction data, Econometrica, 66, 1127-1162. https://doi.org/10.2307/2999632
  12. Ferland, R., Latour, A., and Oraichi, D. (2006). Integer-valued GARCH process, Journal of Time Series Analysis, 27, 923-942. https://doi.org/10.1111/j.1467-9892.2006.00496.x
  13. Fernandez, C. and Steel, M. F. J. (1998). On Bayesian modeling of fat tails and skewness, Journal of the American Statistical Association, 93, 359-371.
  14. Francq, C. and Zakoian, J. M. (2013). Optimal predictions of powers of conditionally heteroscedastic pro-cesses, Journal of Royal Statistical Society B, 75, 345-367. https://doi.org/10.1111/j.1467-9868.2012.01045.x
  15. Glosten, L. R., Jagannathan, R., and Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks, The Journal of Finance, 48, 1779-1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x
  16. Godambe, V. P. (1985). The foundation of finite sample estimation in stochastic processes, Biometrika, 72, 419-428. https://doi.org/10.1093/biomet/72.2.419
  17. Grunwald, G. K., Hyndman, R. J., Tedesco, L., and Tweedie, R. L. (2000). Non-Gaussian conditional linear AR(1) models, Australian and New Zealand Journal of Statistics, 42, 479-495. https://doi.org/10.1111/1467-842X.00143
  18. Hansen, P. R. and Lunde, A. (2005). A forecast comparison of volatility models: does anything beat a GARCH (1, 1)?, Journal of Applied Econometrics, 20, 873-889. https://doi.org/10.1002/jae.800
  19. Heyde, C. C. (1997). Quasi-Likelihood and Its Application, Springer, New York.
  20. Hwang, S. Y., Baek, J. S., Park, J. A., and Choi, M. S. (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
  21. Hwang, S. Y. and Basawa, I. V. (2014). Martingale estimating functions for stochastic processes : A review toward a unifying tool, Contemporary Developments in Statistical Theory, edited by Lahiri et al., Springer, Switzerland, 9-28.
  22. Hwang, S. Y., Basawa, I. V., Choi, M. S., and Lee, S. D. (2014a). Non-ergodic martingale estimating functions and related asymptotics, Statistics, 48, 487-507. https://doi.org/10.1080/02331888.2012.748772
  23. Hwang, S. Y., Choi, M. S., and Yeo, I.-K. (2014b). Quasilikelihood and quasi maximum likelihood for GARCH-type processes: Estimating function approach, Journal of the Korean Statistical Society, 43, 631-641. https://doi.org/10.1016/j.jkss.2014.01.005
  24. Jorion, P. (1997). Value at Risk: The New Benchmark for Controling Market Risk, McGraw-Hill, Chicago.
  25. Kim, H. and Lee, M. (2005). Econometric and Financial Time Series, Kyungmunsa, Seoul.
  26. Lai, T. L. and Xing, H. (2008). Statistical Models and Methods for Financial Markets, Springer, New York.
  27. Lee, J. W., Yoon, J. E., and Hwang, S. Y. (2013). A graphical improvement in volatility analysis for financial series, Korean Journal of Applied Statistics, 26, 785-796. https://doi.org/10.5351/KJAS.2013.26.5.785
  28. Li, W. K. (2004). Diagnostic Checks in Time Series, Chapman & Hall, New York.
  29. Linton, O. B. (2009). Semi-parametric and nonparametric ARCH modeling, in Handbook of Financial Time Series, 157-168, Eds., Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T., Springer, Berlin.
  30. Park, J. A., Baek, J. S., and Hwang, S. Y. (2009). Persistent threshold-GARCH processes: model and application, Statistics & Probability Letters, 79, 907-914. https://doi.org/10.1016/j.spl.2008.11.018
  31. Song, E., Choi, M. S., and Hwang, S. Y. (2008). Volatility analysis for multivariate time series via dimension reduction, Communications of the Korean Statistical Society, 15, 825-835. https://doi.org/10.5351/CKSS.2008.15.6.825
  32. Straumann, D. (2005). Estimation in Conditionally Heteroscedastic Time Series Models, LNS No. 181, Springer, Berlin.
  33. Taylor, S. J. (1994). Modeling stochastic volatility: a review and comparative study, Mathematical Finance, 4, 183-204. https://doi.org/10.1111/j.1467-9965.1994.tb00057.x
  34. Terasvirta, T. (2009). An introduction to univariate GARCH models, In Handbook of Financial Time Series, 17-42, Eds., Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T., Springer, Berlin.
  35. Tong, H. (1990). Nonlinear Time Series, Oxford University Press, Oxford.
  36. Tsay, R. S. (2010). Analysis of Financial Time Series, Third Ed. Wiley, New York.
  37. Wei, W. W. S. (2006). Time Series Analysis, 2nd Ed., Pearson, New York
  38. Xiao, L. (2013). Realized volatility forecasting: empirical evidence from stock market indices and exchange rates, Applied Financial Economics, 23, 57-69. https://doi.org/10.1080/09603107.2012.707769
  39. Yoon, J. E. and Hwang, S. Y. (2015a). Zero-inflated INGARCH using conditional Poisson and negative binomial: data application, Korean Journal of Applied Statistics, 28, 583-592. https://doi.org/10.5351/KJAS.2015.28.3.583
  40. Yoon, J. E. and Hwang, S. Y. (2015b). 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
  41. Zhu, F. (2011). A negative binomial integer-valued GARCH model, Journal of Time Series Analysis, 32, 54-67. https://doi.org/10.1111/j.1467-9892.2010.00684.x
  42. Zhu, F. (2012). Zero-inflated Poisson and negative binomial integer-valued GARCH models, Journal of Statistical Planning and Inference, 142, 826-839. https://doi.org/10.1016/j.jspi.2011.10.002
  43. Zivot, E. (2009). Practical issues in the analysis of univariate GARCH models, In Handbook of Financial Time Series, 113-155, Eds., Andersen, T.G., Davis, R.A., Kreiss, J.-P. and Mikosch, T., Springer, Berlin.