Spectrum estimation is a ubiquitous data analysis technique which finds extensive application in the study of data arising both in econometrics, and in the physical sciences (ranging from electrical engineering and physics to geophysics and oceanography).
This project aims to improve spectrum estimation by use of the wavelet transform. The proposed approach is to take as parameters the integrals of the spectrum over the wavelet octave bands, since these integrated segments will equate to the (scaled) variance of the wavelet coefficients for the corresponding octave bands. The sample variances of the wavelet coefficients will give estimates of the parameters. The research work would consist of exploring the bias, variance and covariance properties of the parameter estimates for different types of process and different types of wavelet filters. In addition to theoretical developments, the research will include the study of both simulated and real time series, and software development.