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.
