Wavelet convolution is a powerful signal processing tool, used on Sigma-L to examine cycles in markets that are changing in power and frequency over time. We look at some of the key features
What to do when spectral analysis results suggest the existence of more cycles in the price series than proposed by Hurst Nominal Model? Ie. I get distinct peaks at:
13 23 27 34 39 45 54 67 81 96 121 157 195 day wave lengths. How do I decide which of those should be dismissed? Because even if I fully trust Hurst's model how do I decide between 34, 39 and 45 or 67 and 81 when all fall close to 40 and 80 respectively? And why 54-day cycle has to be dismissed even though its 2nd harmonic at 27 days is present?
This is the fundamental reason why it is not great to use a static FFT, since the modulation over time is clumped together (temporal information is lost) and the principal reason I use wavelet convolution in my analysis. You will see several peaks because they are power occuring at different times at slightly different frequencies, modulation is constant. The distrubution of that modulation is what you can base a 'model' of 'average' cycle lengths on and what Hurst did. You should not fully trust Hurst's model, I don't, I use a purely objective, evidence based approach as seen in report charts etc on Sigma-L.
What to do when spectral analysis results suggest the existence of more cycles in the price series than proposed by Hurst Nominal Model? Ie. I get distinct peaks at:
13 23 27 34 39 45 54 67 81 96 121 157 195 day wave lengths. How do I decide which of those should be dismissed? Because even if I fully trust Hurst's model how do I decide between 34, 39 and 45 or 67 and 81 when all fall close to 40 and 80 respectively? And why 54-day cycle has to be dismissed even though its 2nd harmonic at 27 days is present?
This is the fundamental reason why it is not great to use a static FFT, since the modulation over time is clumped together (temporal information is lost) and the principal reason I use wavelet convolution in my analysis. You will see several peaks because they are power occuring at different times at slightly different frequencies, modulation is constant. The distrubution of that modulation is what you can base a 'model' of 'average' cycle lengths on and what Hurst did. You should not fully trust Hurst's model, I don't, I use a purely objective, evidence based approach as seen in report charts etc on Sigma-L.
Hi David. May I know what toolbox or code did you use to 3d-plot these wavelets? They look much much prettier than the default ones in Matlab.
Hi Cjin, I use a variety of libraries. The 3d plot above is achieved in unity, amongst others!
Oh I see. Thanks for the article. Really informative and great work for combining Hurst theory with modern signal processing stuff !
Absolutely my pleasure, glad you enjoyed