An Introduction to Wavelets and Other Filtering Methods in Finance and Economics

6

WAVELET DENOISING

6.1 INTRODUCTION

Observed time series are almost never simple objects. The inherent variability of any process produces complicated features that may or may not be present in the underlying signal. Hence, developing techniques to help researchers discriminate the signal from the noise has been of interest as long as measurements have been taken. One avenue of interest is to find an appropriate way to re-express the observed time series. The discrete Fourier transform is a technique with an established history. Its basic premise is that any signal may be expressed as an infinite superposition of sinusoidal functions. This seems ideal for observed processes which have underlying signals that are periodic and globally stationary ...