Estimation of Smoothing Constant of Minimum Variance and its Application to Industrial Data

  • 발행 : 2008.06.30

초록

Focusing on the exponential smoothing method equivalent to (1, 1) order ARMA model equation, a new method of estimating smoothing constant using exponential smoothing method is proposed. This study goes beyond the usual method of arbitrarily selecting a smoothing constant. First, an estimation of the ARMA model parameter was made and then, the smoothing constants. The empirical example shows that the theoretical solution satisfies minimum variance of forecasting error. The new method was also applied to the stock market price of electrical machinery industry (6 major companies in Japan) and forecasting was accomplished. Comparing the results of the two methods, the new method appears to be better than the ARIMA model. The result of the new method is apparently good in 4 company data and is nearly the same in 2 company data. The example provided shows that the new method is much simpler to handle than ARIMA model. Therefore, the proposed method would be better in these general cases. The effectiveness of this method should be examined in various cases.

키워드

참고문헌

  1. Barndoff-Nielsen, O. E. and Shephard, N. (2001), Econometric Analysis of Realised Volatility and Its Use in Estimating Stochastic Volatility Models, Journal of the Royal Statistical Society, 64(B), 253-280.
  2. Box, J. (1994), Time Series Analysis Third Edition. Prentice Hall.
  3. Brown R. G. (1963), Smoothing Forecasting and Prediction of Discrete-Time series. Prentice Hall.
  4. Engle, R. F. (1982), Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50, 987-1008.
  5. Hyndman, R. J., Koehler, A. B., Snyder R. D., and Grose, S. (2002), A State Space framework for Automatic Forecasting using Exponential Smoothing Methods, International Journal of Forecasting, 18, 439- 454.
  6. Ishii, N. A. And Iwata N., Suzumura (1991), Bilateral Exponential Smoothing of Time Series, Int. J. System Sci, 12(8), 997-988.
  7. Jacquer, E., Nicholas, G. P., and Rossi P. E. (2004), Bayesian Analysis of Stochastic Volatility Models with Fat-tails and Correlated Errors, Journal of Econometrics, 122, 185-212.
  8. Johnston, F. R. (1993), Exponentially Weighted Moving Average (EWMA) with Irregular Updating Period, J.Opl.Res.Soc., 44(7), 711-716.
  9. Kern, S. E. (1982), Adaptive Exponential Smoothing Revisited, J.Opl.Res.Soc, 32, 775-782.
  10. Kobayashi, K. (1993), Sales Forecasting for Bugeting. Chuo-Kezaisha Publishing.
  11. Maeda, K. (1984), Smoothing Constant of Exponential Smoothing Method, Seikei University Report Faculty of Engineering, 38.
  12. Makridakis, S. and Winkler, R. L. (1983), Averages of Forecasts, Some Empirical Results. Mgt. Sci, 9.
  13. Makridakis, S., Wheelwright, S. C., and Hyndman, R. J. (1998), Forecasting: Methods and Applications. New York: John Wiley and Sons.
  14. Meyer, R. and Yu, J. (2000), BUGS for a Bayesian Analysis of Stochastic Volatility Models, Econometrics Journal, 3, 198-215.
  15. Takeyasu, K. (1996), System of Production, Sales and Distribution, Chouou-Kezaisha Publishing.
  16. Takeyasu, K. (2002), Estimation of Smoothing Constant in Exponential Smoothing Method, The 4th Asia- Pacific Conference on Industrial Engineering and Management Systems.
  17. Tokumaru, H., et al. (1982), Analysis and Measurement - Theory and Application of Random Data Handling. Baifukan Publishing.
  18. West, M. and Harrison, P. J. (1989), Baysian Forecasting and Dynamic Models. New York: Springer Verlag.
  19. Winter, P. R. (1963). Forecasting Sales by Exponentially Weighted Moving Average, Mgt. Sci., 6(3).