Arithmetic Return Model for Removing Autocorrelation from Data Exhibiting Geometric Brownian Motion

Abstract

The presence of positive autocorrelation in a controlled process is a major problem especially when traditional quality control charts are to be used in monitoring the process. This is because the two major assumptions in using the traditional control charts are that the process data are independently and normally distributed. In this work, a novel method of removing autocorrelation from data exhibiting Geometric Brownian Motion (GBM) is proposed. This GBM is autoregressive of order AR(1). A chemical process dataset and furnace temperature dataset were transformed to Arithmetic Return model (ARM). The fitted ARM for both datasets were fitted and residuals obtained from both datasets were subjected to DW test for the presence of positive autocorrelation. Initial Durbin Watson’s (DW) test result for both processes before the transformation were 0.0538 and 1.5045 respectively which indicated the presence of positive autocorrelation. Final DW test results from the ARM transformation were 2.0047 and 1.7848 respectively indicating that positive autocorrelation was removed from both datasets. The proposed method is simple to understand and easy to use provided that the process data is GBM and autocorrelation is the major concern.