The Performance Characterization of Discrete Kalman Filter under the First Order Autoregressive Demands

Abstract

The accuracy of forecasting is important to the performance of supply chain systems. This research focuses on the demand which is stationary. Since Box-Jenkin’s first order autoregressive model or AR (1) is widely used to characterize the stationarity, the data in this research is simulated on the basis of the AR (1) model. Moreover, because Kalman filter is a recursive technique used to forecast the observation, the objective is to facilitate the utilization of Kalman filter by practitioners. The empirical study is conducted to characterize the performance of Kalman filter when the structure of observations follows AR (1) model. Due to the experimental results, the different degrees of stationarity are adjusted by controlling the values of autoregressive coefficients ( f ). Afterwards, Kalman filter is applied to forecast the simulated data while the forecasting errors in term of minimum average percentage error (MAPE) are calculated. The results indicate that Kalman filter should work at its best when the autoregressive coefficient is highly positive. After the assessment, the application of Kalman filter to AR (1) observations is completely standardized so it provides the procedures and guidelines for practitioners when dealing with the stationary process.