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0.3 Wavelet analysis: a new approach

The path to a solution

To try to solve some of the problems caused by taking an inconclusive transform of a whole time series, Dennis Gabor developed Short-Time Fourier Analysis on windowed signals in 1946. However, this approach offered no variability to determine time or frequency more accurately in any particular window. Wavelet analysis was developed as a windowing technique which allowed for differently-sized windows to be compared to a wavelet signal, therefore allowing determination of time AND frequency. The basic premise is derived from Fourier transforms, but instead of composing a signal of different frequency and amplitude sinusoids, wavelets of the same waveform but different lengths are compared and correlated to a signal.

Wavelet analysis has many benefits which make it a more applicable tool for analyzing the financial markets. This:

uses long -time wavelet-analysis intervals for finding precise low -frequency information.
uses short -time wavelet-analysis intervals for finding precise high -frequency information.
performs local analysis, which allows us see frequency events at a specific times in a signal.
works much better with non-linear signals.

This is an example of wavelet analysis applied to sunspot size. The pattern indicates a few patterns, the most prevalent of which is a cycle of roughly 11 years.

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Read also:

OpenStax, Wavelet analysis of crude oil futures. OpenStax CNX. Dec 19, 2011 Download for free at http://cnx.org/content/col11397/1.1

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