The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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EMD based hybrid models to forecast the KOSPI

코스피 예측을 위한 EMD를 이용한 혼합 모형

  • Kim, Hyowon (Department of Applied Statistics, Chung-Ang University) ;
  • Seong, Byeongchan (Department of Applied Statistics, Chung-Ang University)
  • 김효원 (중앙대학교 응용통계학과) ;
  • 성병찬 (중앙대학교 응용통계학과)
  • Received : 2016.02.26
  • Accepted : 2016.02.29
  • Published : 2016.04.30
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Abstract

The paper considers a hybrid model to analyze and forecast time series data based on an empirical mode decomposition (EMD) that accommodates complex characteristics of time series such as nonstationarity and nonlinearity. We aggregate IMFs using the concept of cumulative energy to improve the interpretability of intrinsic mode functions (IMFs) from EMD. We forecast aggregated IMFs and residue with a hybrid model that combines the ARIMA model and an exponential smoothing method (ETS). The proposed method is applied to forecast KOSPI time series and is compared to traditional forecast models. Aggregated IMFs and residue provide a convenience to interpret the short, medium and long term dynamics of the KOSPI. It is also observed that the hybrid model with ARIMA and ETS is superior to traditional and other types of hybrid models.

본 연구에서는 시계열 자료의 비정상성과 비선형성과 같은 복잡성을 효과적으로 포용할 수 있는 경험적모드분해법(empirical mode decomposition; EMD)을 토대로 시계열 자료의 분석 및 예측을 위한 혼합(hybrid) 모형을 연구한다. EMD에 의하여 생성되는 내재모드함수(intrinsic mode function; IMF)는 해석 및 예측의 편리성을 개선하기 위하여 누적에너지의 개념을 사용하여 그룹화하였으며, 그룹화된 IMF 및 residue의 성분들은 그 성질에 따라서 ARIMA 모형 및 지수평활법과 결합된 혼합 모형으로 예측된다. 제안된 방법은 일별 코스피 지수의 예측을 위해서 적용하였다. 다양한 형태의 혼합 모형을 사용하여 코스피 지수를 예측하였으며 전통적인 예측 방법과 비교하였다. 분석 결과, 그룹화된 성분들은 코스피 지수의 움직임을 단기적, 중기적, 장기적으로 해석하는데 편리함을 주었으며, 그룹화된 IMF 및 residue를 각각 ARIMA 모형과 지수평활법으로 조합한 혼합 모형이 우수한 예측력을 보여주었다.

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References

  1. Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1993). Time Series Analysis: Forecasting and Control, Prentice Hall, New Jersey.
  2. Brown, R. G. (1959). Statistical Forecasting for Inventory Control, McGraw-Hill, New York.
  3. De Livera, A. M., Hyndman, R. J., and Snyder, R. D. (2011). Forecasting time series with complex seasonal patterns using exponential smoothing, Journal of the American Statistical Association, 106, 1513-1527. https://doi.org/10.1198/jasa.2011.tm09771
  4. Gould, P. G., Koehler, A. B., Ord, J. K., Snyder, R. D., Hyndman, R. J., and Vahid-Araghi, F. (2008). Forecasting time series with multiple seasonal patterns, European Journal of Operational Research, 191, 207-222. https://doi.org/10.1016/j.ejor.2007.08.024
  5. Holt, C. C. (1957). Forecasting trends and seasonals by exponentially weighted moving average, Office of Naval Research, Research Memorandum, 52, Carnegie Institute of Technology.
  6. Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C., and Liu, H. H. (1998). The empirical mode decomposition and Hilbert spectrum for nonlinear and nonstationary time series analysis, In Proceeding of the Royal Society London A, 454, 903-995. https://doi.org/10.1098/rspa.1998.0193
  7. Hyndman, R. J. and Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for R, Journal of Statistical Software, 26, 1-22.
  8. Kim, D. and Oh, H.-S. (2009). A multi-resolution approach to non-stationary financial time series using the Hilbert-Huang transform, The Korean Journal of Applied Statistics, 22, 499-513. https://doi.org/10.5351/KJAS.2009.22.3.499
  9. Kim, D., Paek, S.-H., and Oh, H.-S. (2008). A Hilbert-Huang transform approach for predicting cyber-attacks, Journal of the Korean Statistical Society, 27, 277-283.
  10. Park, M. and Seong, B. (2014). Comparison of EMD and HP filter for cycle extraction, The Korean Journal of Applied Statistics, 27, 431-444. https://doi.org/10.5351/KJAS.2014.27.3.431
  11. Wei, W. W. (2006). Time Series Analysis, 2nd ed., Addison-Wesley, Redwood City, California.
  12. Wei, Y. and Chen, M.-C. (2012). Forecasting the short-term metro passenger ow with empirical mode decomposition and neural networks, Transportation Research Part C, 21, 148-162. https://doi.org/10.1016/j.trc.2011.06.009
  13. Winters, P. R. (1960). Forecasting sales by exponentially weighted moving averages, Management Science, 6, 324-342. https://doi.org/10.1287/mnsc.6.3.324
  14. Zhu, B., Wang, P., Chevallier, J., and Wei, Y. (2015). Carbon price analysis using empirical mode decomposition, Computational Economics, 45, 195-206. https://doi.org/10.1007/s10614-013-9417-4