PARAMETER ESTIMATION OF ARIMA USING GOAL PROGRAMMING

Abstract

Goal programming (GP) is an improved technique of the linear programming model that is suitable for multi-criteria decision making for organizations that have multiple objectives that are usually not measurable in the same units. Autoregressive integrated moving average model (ARIMA) is useful in predicting future behavior based on past behaviors. It is also useful for forecasting when there is any relationship between values especially in a time series in nature, the values before and the values after them. In this paper, we examine the application of goal programming as a mathematical tool for estimating the parameters of time series forecasting models such as the estimation of ARIMA model’s parameters using traditional estimation and goal programming. Ordinary Least Squares (OLS) is used to estimate the ARIMA parameters using a linear constrained goal programming set. Maximum likelihood estimation and goal programming methods have been studied and compared using mean absolute error (MAE). We show that the GP prediction's mean absolute error values in the data set were significantly lower than those attained by the ARIMA model. These findings suggest that the prediction equations derived by goal programming were more accurate than those generated through maximum likelihood estimation. This can be formulated as minimizing the sum of absolute errors using goal programming as opposed to the ARIMA model's sum of squares error.