Modeling positive time series data: a neglected aspect in time series courses

Abstract

Something has been forgotten in time series courses, in particular, when dealing with positive datasets. To describe the pattern hidden in this type of datasets, before we use a sophisticated method of modeling such as Autoregressive Integrated Moving Average (ARIMA), we propose to check first whether the data represent a Geometric Brownian Motion (GBM) process. If it is affirmative, unlike the other methods, the method of GBM time series modeling might provide the desired model in a simple and easy to digest procedure with cheaper cost and high speed of computation. Because of its simplicity and practicality, even non-statisticians who have a very limited background in statistics could take easily the fruit and benefit of this method. In this study, unlike the standard approach that can be found in the literature, GBM process will be approached from log-normal process. This is the first result of this paper which shows the simplicity of GBM process. To identify this process, as a strong indication that a process is GBM process, we can see the value of the serial correlation. The smaller the serial correlation of log returns the higher the tendency that the process is GBM process. As the second result, for practical purposes, a new procedure of time series modeling if data are positive will be introduced. These results show that, when dealing with positive dataset, GBM time series modeling is worthwhile to be included in any introductory Time Series course especially for non-statistics students. To illustrate the practical advantages of GBM time series modeling, real case studies from industries as well as government agencies and internet will be presented and discussed.