A Modeling Methodology for Positive Autocorrelated Process Data

Autocorrelated statistical process control that is widely employed in process control environments typically uses the autoregressive integrated moving average (ARIMA) model in fitting autocorrelated time series data. Nevertheless, ARIMA entails laborious iterative modeling procedures and is commented as time-consuming, expensive, and complex. Meanwhile, autocorrelated data is governed by the geometric Brownian motion (GBM) law if its logarithmic returns are independent and identically normally distributed (i.i.n.d.). By utilizing these attributes, this paper aims to propose an alternative methodology in modeling time series data by applying the Logarithmic Return (LR) model. To demonstrate the applicability of the proposed model, it is used to fit a cocoa powder dataset. In addition to being parsimonious and easy to compute, the LR model is reported with shorter Central Processing Unit (CPU) running time, that is it takes an average of less than 0.20 seconds to obtain the LR model meanwhile more than 5 seconds are needed by its counterpart. LR model has a comparable good mean average percentage error (MAPE) to the ARIMA model, thus LR model is as accurate as the ARIMA model. All computations are implemented via R - programming language. This study shows that the LR model with two parameters and requires a two-step implementation procedure is a promising alternative model of ARIMA for positive datasets in time series modeling.