Geometric brownian motion approaches for modeling daily maximum electricity load demand in Peninsular Malaysia

Abstract

This research is about statistical modeling of geometric Brownian motion (GBM) process of daily maximum electricity load demand based on one year data set starting from 1st September 2005 until 31st August 2006. The distributional behavior and the existence of autocorrelation in the whole time series data had caused problem in terms of building the most appropriate model rather than just using a satisfactory model for forecasting analysis. In literature, modeling for forecasting the electricity load demand that involves calendar effects is difficult to be appropriately modeled using the pure time series model. This difficulty is due to the random occurrences of public holidays in Malaysia; there are public holidays that do not fall on the same date and day every year. This occurrence is hard to handle and will cause the pattern of electricity load demand to vary every year. According to the time series data in Malaysia, the term “days” are clustered into three clusters. The clusters are the proximity day and state holiday group, the weekend and holiday group, and working day group. It is this distributional data pattern in each cluster that makes the construction of an appropriate forecasting model for the whole data more difficult. The main problem is that the data does not distribute normally in every cluster although transformation technique such as Box-Cox had been used on the whole data at the begining of this research. The time series data are required to follow normal distribution because some models or methods in forecasting analysis can only performed at its best only in this condition. This initial findings lead to the implementation of GBM process in each cluster as the mathematical law proposed by GBM can be tested in terms of building an appropriate model for the data, the GBM model. Time series data that are governed by GBM will tend to be independent with following normal distributions. The advantages of this model are presented by comparing its performance to those issued from ARMA and ARIMA model. Performance of GBM model is better among the tested models by giving smallest MAPE residuals which proved to be highly accurate model for the time series data used