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

5

WAVELETS AND STATIONARY PROCESSES

5.1 INTRODUCTION

In the latter part of the twentieth century, several disciplines came to the realization that naturally occurring phenomena (river flow, atmospheric patterns, telecommunications, astronomy, financial markets, etc.) exhibit correlations that do not decay at a sufficiently fast rate. This means that observations separated by great periods of time still exhibit significant correlation. These time series are known as long-memory or long-range dependent processes and require different approaches to modeling than the so-called short-memory time series. At first, Fourier-based methods dominated the literature in terms of identifying and fitting models to long-memory processes. Wavelets have shown ...