Estimation of Smoothing Constant of Minimum Variance Searching Optimal Parameters of Weight

Focusing that the equation of exponential smoothing method (ESM) is equivalent to (1,1) order ARMA model equation, a new method of estimation of smoothing constant in exponential smoothing method was proposed before by us which satisfied minimum variance of forecasting error.Generally, smoothing constant is selected arbitrarily.But in this paper, we utilize above stated theoretical solution.Firstly, we make estimation of ARMA model parameter and then estimate smoothing constants.Thus theoretical solution is derived in a simple way and it may be utilized in various fields.Furthermore, combining the trend removing method with this method, we aim to improve forecasting accuracy.Trend removing by the combination of linear and 2nd order non-linear function and 3rd order non-linear function is executed to the original shipping data of consumer goods.The weights for these functions are varied by 0.01 increment and optimal weights are searched.For the comparison, monthly trend is removed after that.Theoretical solution of smoothing constant of ESM is calculated for both of the monthly trend removing data and the non monthly trend removing data.The new method shows that it is useful for the time series that has monthly trend characteristics and we have obtained some interesting results.