The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

LIHAR model for forecasting realized volatilities featuring long-memory and asymmetry

장기기억성과 비대칭성을 띠는 실현변동성의 예측을 위한 LIHAR모형

  • Shin, Jiwon (Department of Statistics, Ewha Womans University) ;
  • Shin, Dong Wan (Department of Statistics, Ewha Womans University)
  • 신지원 (이화여자대학교 통계학과) ;
  • 신동완 (이화여자대학교 통계학과)
  • Received : 2016.07.15
  • Accepted : 2016.09.14
  • Published : 2016.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Cho and Shin (2016) recently demonstrated that an integrated HAR model has a forecast advantage over the HAR model of Corsi (2009). Recalling that realized volatilities of financial assets have asymmetries, we add a leverage term to the integrated HAR model, yielding the LIHAR model. Out-of-sample forecast comparisons show superiority of the LIHAR model over the HAR and IHAR models. The comparison was made for all the 20 realized volatilities in the Oxford-Man Realized Library focusing specially on the DJIA, the S&P 500, the Russell 2000, and the KOSPI. Analysis of the realized volatility data sets reveal apparent long-memory and asymmetry. The LIHAR model takes advantage of the long-memory and asymmetry and produces better forecasts than the HAR, IHAR, LHAR models.

최근에 Cho와 Shin (2016)가 변동성 예측 모형으로 유명한 HAR (Corsi, 2009) 모형보다 단위근을 부과한 IHAR 모형이 더 우수하다는 것이 보고하였다. 금융시계열에 비대칭 변동성이 존재한다는 것은 널리 알려져 있다. 이 논문에서는 IHAR 모형에 레버리지를 고려한 LIHAR 모형을 제안한다. LIHAR 모형과 IHAR 모형 기존의 HAR 모형, LHAR 모형과의 예측력 비교를 통해 LIHAR 모형의 우수성을 보인다. 모형을 평가하기 위해 Oxford-Man 라이브러리 20개의 실현변동성 데이터를 이용하였다. 특히 DJIA, S&P 500, Russell 2000, KOSPI Composite 데이터는 다양한 분석을 하였다. 주가와 같은 금융지수의 변동성에는 장기기억성과 비대칭 변동성이 존재하고, 이런 특징을 LIHAR 모형이 HAR, IHAR, LHAR 모형보다 적절하게 반영하고 있는 것을 확인 하였다. 또한 예측력도 LIHAR 모형이 가장 우수하였다. 금융시계열의 실현변동성에 장기기억성, 비대칭변동성, 비정상성을 모두 반영하여 예측하는 것이 상당한 가치가 있음을 확인하였다.

Keywords

References

  1. Andersen, T. G. and Bollerslev, T. (1997). Heterogeneous information arrivals and return volatility dynamics: uncovering the long-run in high frequency returns, The Journal of Finance, 52, 975-1005. https://doi.org/10.1111/j.1540-6261.1997.tb02722.x
  2. Andersen, T. G., Bollerslev, T., Diebold, F. X., and Ebens, H. (2001). The distribution of realized stock return volatility, Journal of Financial Economics, 61, 43-76. https://doi.org/10.1016/S0304-405X(01)00055-1
  3. Andersen, T. G., Bollerslev, T., and Meddahi, N. (2005). Correcting the errors: volatility forecast evaluation using high-frequency data and realized volatilities, Econometrica, 73, 279-296. https://doi.org/10.1111/j.1468-0262.2005.00572.x
  4. Andersen, T. G., Bollerslev, T., and Meddahi, N. (2011). Realized volatility forecasting and market microstructure noise, Journal of Econometrics, 160, 220-234. https://doi.org/10.1016/j.jeconom.2010.03.032
  5. Asai, M., McAleer, M., and Medeiros, M. C. (2012). Asymmetry and long memory in volatility modeling, Journal of Financial Econometrics, 10, 495-512. https://doi.org/10.1093/jjfinec/nbr015
  6. Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics, Journal of Econometrics, 73, 5-59. https://doi.org/10.1016/0304-4076(95)01732-1
  7. Banerjee, A. and Urga, G. (2005). Modelling structural breaks, long memory and stock market volatility: an overview, Journal of Econometrics, 129, 1-34. https://doi.org/10.1016/j.jeconom.2004.09.001
  8. Bekaert, G. and Wu, G. (2000). Asymmetric volatility and risk in equity markets, The Review of Financial Studies, 13, 1-42. https://doi.org/10.1093/rfs/13.1.1
  9. Bisaglia, L. and Procidano, I. (2002). On the power of the augmented Dickey-Fuller test against fractional alternatives using bootstrap, Economics Letters, 77, 343-347. https://doi.org/10.1016/S0165-1765(02)00146-5
  10. Campbell, J. Y. and Hentschel, L. (1992). No news is good news: an asymmetric model of changing volatility in stock returns, Journal of Financial Economics, 31, 281-318. https://doi.org/10.1016/0304-405X(92)90037-X
  11. Chiriac, R. and Voev, V. (2011). Modelling and forecasting multivariate realized volatility, Journal of Applied Econometrics, 26, 922-947. https://doi.org/10.1002/jae.1152
  12. Cho, S. and Shin, D. W. (2016). An integrated heteroscedastic autoregressive model for forecasting realized volatilities, Journal of the Korean Statistical Society, 45, 371-380. https://doi.org/10.1016/j.jkss.2015.12.004
  13. Christie, A. A. (1982). The stochastic behavior of common stock variances: value, leverage and interest rate effects, Journal of Financial Economics, 10, 407-432. https://doi.org/10.1016/0304-405X(82)90018-6
  14. Corsi, F. (2004). A simple long memory model of realized volatility, Available from: http://dx.doi.org/10.2139/ssrn.626064
  15. Corsi, F. (2009). A simple approximate long-memory model of realized volatility, Journal of Financial Econometrics, 7, 174-196.
  16. Corsi, F., Audrino, F., and Reno, R. (2012). HAR modeling for realized volatility forecasting, Handbook of Volatility Models and Their Applications (pp. 363-382), John Wiley & Sons, New Jersey.
  17. Corsi, F. and Reno, R. (2009). HAR volatility modelling with heterogeneous leverage and jumps, Available from: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.375.5804&rep=rep1&type=pdf
  18. Corsi, F., Zumbach, G., Muller, U. A., and Dacorogna, M. M. (2001). Consistent high-precision volatility from high frequency data, Economic Notes, 30, 183-204. https://doi.org/10.1111/j.0391-5026.2001.00053.x
  19. Dacorogna, M. M., Muller, U. A., Nagler, R. J., Olsen, R. B., and Pictet, O. V.(1993). A geographical model for the daily and weekly seasonal volatility in the foreign exchange market, Journal of International Money and Finance, 12, 413-438. https://doi.org/10.1016/0261-5606(93)90004-U
  20. Deo, R., Hurvich, C., and Lu, Y. (2006). Forecasting realized volatility using a long-memory stochastic volatility model: estimation, prediction and seasonal adjustment, Journal of Econometrics, 131, 29-58. https://doi.org/10.1016/j.jeconom.2005.01.003
  21. Dickey, D. A. and Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root, Journal of the American Statistical Association, 74, 427-431.
  22. Diebold, F. X. and Mariano, R. S. (1995). Comparing predictive accuracy, Journal of Business & Economic Statistics, 13, 134-144.
  23. Ding, Z. and Granger, C. W. (1996). Modeling volatility persistence of speculative returns: a new approach, Journal of Econometrics, 73, 185-215. https://doi.org/10.1016/0304-4076(95)01737-2
  24. Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50, 987-1007. https://doi.org/10.2307/1912773
  25. Engle, R. F. and Ng, V. K. (1993). Measuring and testing the impact of news on volatility, The Journal of Finance, 48, 1749-1778. https://doi.org/10.1111/j.1540-6261.1993.tb05127.x
  26. Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models, Journal of Time Series Analysis, 4, 221-238. https://doi.org/10.1111/j.1467-9892.1983.tb00371.x
  27. 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
  28. Goncalves, S. and Meddahi, N. (2009). Bootstrapping realized volatility, Econometrica, 77, 283-306. https://doi.org/10.3982/ECTA5971
  29. Granger, C. W. and Joyeux, R. (1980). An introduction to long-memory time series models and fractional differencing, Journal of Time Series Analysis, 1, 15-29. https://doi.org/10.1111/j.1467-9892.1980.tb00297.x
  30. Huang, X. and Tauchen, G. (2005). The relative contribution of jumps to total price variance, Journal of Financial Econometrics, 3, 456-499. https://doi.org/10.1093/jjfinec/nbi025
  31. Hurvich, C. M., Deo, R., and Brodsky, J. (1998). The mean squared error of Geweke and Porter-Hudak's estimator of the memory parameter of a long-memory time series, Journal of Time Series Analysis, 19, 19-46. https://doi.org/10.1111/1467-9892.00075
  32. Hwang, E. and Shin, D. W. (2014). Infinite-order, long-memory heterogeneous autoregressive models, Computational Statistics & Data Analysis, 76, 339-358. https://doi.org/10.1016/j.csda.2013.08.009
  33. Kwiatkowski, D., Phillips, P. C., Schmidt, P., and Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root?, Journal of Econometrics, 54, 159-178. https://doi.org/10.1016/0304-4076(92)90104-Y
  34. Martens, M., Van Dijk, D., and De Pooter, M. (2009). Forecasting S&P 500 volatility: long memory, level shifts, leverage effects, day-of-the-week seasonality, and macroeconomic announcements, International Journal of Forecasting, 25, 282-303. https://doi.org/10.1016/j.ijforecast.2009.01.010
  35. McAleer, M. and Medeiros, M. C. (2008). A multiple regime smooth transition heterogeneous autoregressive model for long memory and asymmetries, Journal of Econometrics, 147, 104-119. https://doi.org/10.1016/j.jeconom.2008.09.032
  36. Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: a new approach, , Econometrica, 59, 347-370. https://doi.org/10.2307/2938260
  37. Park, S. and Shin, D. W. (2014). Modeling and forecasting realized volatilities of Korean financial assets featuring long memory and asymmetry, Asia-Pacific Journal of Financial Studies, 43, 31-58. https://doi.org/10.1111/ajfs.12039
  38. Patton, A. J. and Sheppard, K. (2015). Good volatility, bad volatility: signed jumps and the persistence of volatility, Review of Economics and Statistics, 97, 683-697. https://doi.org/10.1162/REST_a_00503
  39. Robinson, P. M. (1995). Log-periodogram regression of time series with long range dependence, The Annals of Statistics, 23, 1048-1072. https://doi.org/10.1214/aos/1176324636
  40. Shephard, N. and Sheppard, K. (2010). Realising the future: forecasting with high-frequency-based volatility (HEAVY) models, Journal of Applied Econometrics, 25, 197-231. https://doi.org/10.1002/jae.1158
  41. Song, H. and Shin, D. W. (2015). Long-memories and mean breaks in realized volatilities, Applied Economics Letters, 22, 1273-1280. https://doi.org/10.1080/13504851.2015.1013605
  42. Soucek, M. and Todorova, N. (2014). Realized volatility transmission: the role of jumps and leverage effects, Economics Letters, 122, 111-115. https://doi.org/10.1016/j.econlet.2013.11.007
  43. Todorov, V., Tauchen, G., and Grynkiv, I. (2011). Realized Laplace transforms for estimation of jump diffusive volatility models, Journal of Econometrics, 164, 367-381. https://doi.org/10.1016/j.jeconom.2011.06.016
  44. Yun, S. and Shin, D. W. (2015). Forecasting the realized variance of the log-return of Korean won US dollar exchange rate addressing jumps both in stock-trading time and in overnight, Journal of the Korean Statistical Society, 44, 390-402. https://doi.org/10.1016/j.jkss.2014.11.001