Abstract

We proposed earlier that the equation of the exponential smoothing method (ESM) is equivalent to (1,1) ARMA model equation, a new method of estimating the smoothing constant in the exponential smoothing method which satisfied the minimum variance of forecasting error. Generally, the smoothing constant is selected arbitrarily, but in this paper, we utilize the above theoretical solution. Firstly, we estimate the ARMA model parameter and then estimate the smoothing constants. Thus, the theoretical solution is derived in a simple way and it may be utilized in various fields. Furthermore, combining the trend removal method with this method, we aim to improve forecasting accuracy. An approach to this method is executed in the following method. Trend removal by the combination of linear, 2nd order non-linear function and 3rd order non-linear function is executed on the stock market price data of J-REIT (Japan Real Estate Investment Trust) for office type. Genetic algorithm is utilized to search optimal weights for the weighting parameters of linear and non-linear function. For the comparison, monthly trend is removed after that. Theoretical solution of the smoothing constant of ESM is calculated for both the monthly trend removal data and the non monthly trend removing data. Then the forecasting is executed on these data. This new method shows that it is useful for the time series that has various trend characteristics. The effectiveness of this method should be examined in various cases.

Key words: Minimum variance, exponential smoothing method, forecasting, trend, genetic algorithm.