Abstract

Wavelets are relatively recent tools in scientific research. Apart from being powerful tools in signal analysis, wavelets are currently being applied in the context of many disciplines. The efficiency of the algorithms and the elegance of the mathematical structures of the wavelet method make it a viable tool in research areas where signal extraction is applicable. In the context of time series inference, the research made use of wavelet-based estimators and tests as a unified and adaptive way of analyzing time series problems. Pertinent theory and formulations were presented under parametric, semi-parametric and non-parametric settings. Computing and applications was demonstrated using wavelab procedures running on MATLAB 5.0 for Windows. Problem applications for this research included analyzing economic and financial time series, specifically those that admit nonlinear structures, as well as deseasonalization. Theoretical formulation and applications with respect to analyzing currency and financial markets was also included.