Has spectrum analysis ever been used successfully to analyse historical price data?

Question

Spectrum analysis is often used to analyse waveforms. A common configuration, for example, is to create a graph where X is time, Y is frequency, and the brightness of each position represents amplitude.

Has spectrum analysis ever been used successfully as an indicator to analyse historical price data, for example the price of shares over time?

Answer 1

I would recommend Marc Wildi's work on signal extraction.

Answer 2

Yes. Check out Time-Series Analysis by Shumway and Stoffer. Spectral Analysis and Filtering is covered in Chapter 4.

Answer 3

Fractal spectra are covered in Multifractal Volatility: Theory, Forecasting, and Pricing. Also note that your run-of-the-mill moving average of a price series is a low-pass filter (filters out the higher frequencies), and moving averages are very used in basic financial analysis.

Answer 4

Here is a gentle introduction to wavelet methods.

Answer 5

Something like a moving average smoother is akin to a low pass filter, the 'stochastics' of technical analysis crudely akin to a band pass filter. Going up the ladder of sophistication, you can see something like http://www.jstor.org/pss/3592665 or applications of wavelet decomposition.

This paper from 1963 by GRANGER, CLIVE W. J., and MORGENSTERN, 0. titled “Spectral Analysis of New York Stock Market Prices,” Kyklos, XVI (January, 1963), I-27 should convince you that people have been more than thinking of applying frequency-domain analysis to this.

Answer 6

Singular Spectrum Analysis ( SSA ) is a relatively new technique ( although Lorenz suggested something similar 1956 ) that is starting to be more widely used. The jury is still out on just how much underlying structure, if any, there actually is in financial time series. Nonetheless a very powerful and easy to use data smoothing and filtering/de-noising technique. A very basic Excel and VBA demonstration available here

Answer 7

I have considered applying Fourier transforms to smoothed Financial and Econometric data but until someone pays me to do it I don't have time. I haven't seen much coverage in the usual complex analysis texts of usage in Financial markets but that is probably because they are more concerned with physical applications. I am also a bit out of date currently, I still use Whittacker and Watson (1902)!