On The Validity of The Geometric Brownian Motion Assumption

Abstract

The geometric Brownian motion (GBM) process is frequently invoked as a model for such diverse quantities as stock prices, natural resource prices and the growth in demand for products or services. We discuss a process for checking whether a given time series follows the GBM process. Methods to remove seasonal variation from such a time series are also analyzed. Of four industries studied, the historical time series for usage of established services meet the criteria for a GBM; however, the data for growth of emergent services do not.