Estimation of Smoothing Constant in Exponential Smoothing Method and Its Expansion : Examination for Extended ESM

Since the equation of exponential smoothing method (ESM) is equivalent to (1,1) order ARMA model equation (or (0,1,1) order ARIMA model), new estimation method of smoothing constant in exponential smoothing method is proposed. Firstly, we make estimation of ARMA model parameter and then estimate smoothing constants. Thus we get theoretical solution by a simple way. New method is examined by applying to the sales data. Useful results are obtained. The score range of coefficient of autocorrelation function is limited for the solution. Therefore expanding the score range, extended ESM in which parameter varies expansively from the customary permitted range is examined and their handling method is proposed.