Wavelet analysis as an alternative approach to model demand time series

Abstract

In this dissertation, we study the wavelet analysis as an alternative approach to the classical SARIMA models for demand time series. Wavelet analysis mainly utilizes two functions, the scaling and wavelet filters, permitting the signal to be analyzed at both its low and high frequency components simultaneously, under different time-scales. These filters allow to capture specific components, such as trend and seasonality, of the original time series. In this study, the discrete wavelet transform(DWTT) is used to decompose a noisy demand time series and to remove the noise from the raw time series, leading to the extraction of any deterministic components. The importance of the wavelet function and decomposition level chosen to perform the DWTT is established in this study. The DWTT is studied to improve the modeling of demand time series using the commonly used Box-Jenkins methods. Comparisons of the two approaches were performed using two demand time series; the Malta power generation, and the demand of a particular tablet manufactured by a local pharmaceutical company. The pros and cons of the DWTT approach for decomposing a time series are presented in this study.