Using wavelets to estimate the long memory parameter and detect long memory phenomena in the presence of deterministic trend

The objective of this dissertation is to study ways of modeling a long memory process using wavelet analysis. The modeling of long memory processes is a new breach of time series analysis. During last twenty years, the long memory phenomena have been found in many applied fields. The observed time series exhibit a persistence of correlation much longer than that explained by a short memory process (e.g. ARIMA). The traditional techniques used to analyze time series data are based on time domain and/or frequency domain, e.g. autocorrelation function and Fourier spectrum analysis. These traditional methods have trouble capturing the long memory phenomena. Wavelets, similar to Fourier transforms, are based on scale and time domain, and provide better opportunities for analyzing long memory data.; The inspiration for working on this thesis came from attempts to model the body temperature of heat challenged steers. This dissertation examines methods of estimating the long memory parameter and a new estimation method using wavelets is proposed. Work has also been done on developing model selection criteria. Methods are proposed for selecting the best long memory model from a list of potential candidates. Another complication in estimating the long memory parameter is the possible presence of a deterministic trend. Methods of estimation in the presence of a deterministic trend are examined and a new optimization criteria for estimating the trend in the presence of FARIMA (0, d, 0) error is proposed. SAS programs were written to test and apply the theory developed.