- Volume 29 Issue 3
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.
intrinsic mode function;exponential smoothing method;ARIMA model;nonstationary model;nonlinear model
- Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1993). Time Series Analysis: Forecasting and Control, Prentice Hall, New Jersey.
- Brown, R. G. (1959). Statistical Forecasting for Inventory Control, McGraw-Hill, New York.
- 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
- 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
- Holt, C. C. (1957). Forecasting trends and seasonals by exponentially weighted moving average, Office of Naval Research, Research Memorandum, 52, Carnegie Institute of Technology.
- 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
- Hyndman, R. J. and Khandakar, Y. (2008). Automatic time series forecasting: the forecast package for R, Journal of Statistical Software, 26, 1-22.
- 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
- 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.
- 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
- Wei, W. W. (2006). Time Series Analysis, 2nd ed., Addison-Wesley, Redwood City, California.
- 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
- 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
- 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
Supported by : Chung-Ang University