Algorithm For Finding The Smallest Mean Square Error In Exponential Smoothing Method For Time Series Forecasting Alfian (1), Muh. Kabil Djafar (1), Nerru Pranuta Murnaka (2), Sulistiawati (2), Rinda Nariswari (3), and Samsul Arifin (3)
1) Mathematics Department, Halu Oleo University, Kendari Indonesia 93232
2) Mathematics Education Department, STKIP Surya, Tangerang, Indonesia 15115
3) Statistics Department, School of Computer Science, Bina Nusantara University, Jakarta, Indonesia 11480
Abstract
One of the measurements for evaluating time series forecasting performances is the mean square error (MSE). This paper proposes the algorithm to find the smallest MSE. To capture four components of time series data (that are seasonal variations, trend variations, cyclical variations, random variations), exponential smoothing method is used. This method uses three factors for smoothing where apha is the data smoothing factor, 0 < apha < 1, betha is the trend smoothing factor, 0 < betha < 1, and gamma is the seasonal change smoothing factor, 0 < gamma < 1. All possible combinations values of smoothing factors will be generated to three decimal digits. After that, the smallest MSE of those combinations will be determined with using an algorithm and then to observe the convergence pattern of them.
Keywords: Algorithm, Smallest Mean Square Error, Exponential Smoothing Method
