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A-Trous Wavelet Transform

Introduction

(Excellent FastFourier and Wavelet tutorial for engineers here)

There has been a lot of hype around the use of wavelets to better analyze the behavior of financial instruments.  Studies have proven the chaotic and fractal nature of financial markets, but apart from wavelet transforms, little has been done to turn these powerful concepts into useable trading tools.  Yet, wavelets are probably nowadays the most powerful tools available to extract underlying trends in financial series. 

Wavelets are non linear tools, so indeed do not share some of the limitations of (Fast) Fourier Transform, however many wavelet transforms are still unsuitable for financial series.  FFT is basically (imho) a waste of time unless stable cycles can be found in price movements, and wavelets, whilst a powerful concept, are no easy answer either.  We're not out of the woods yet... There are many filter banks, and most were developed with 2D/3D space in mind, and are poorly converted to work with time series.  Even with this type of wavelet, end point distortion remains an important issue.

Wouldn't it just be so much easier if at any point in time one could know both sides to calculate the wavelet transform more accurately?  Well, not only knowing a bit of past and future at any point time would facilitate the calculations, but we would not need wavelets to make money, wouldn't we?

There have been many attempts to alleviate that problem, and we do not feel we are in the position to judge nor compare most of them.  There is the Morlet flavour (cf WaveFin as a possible reference), which will not be discussed here, but is also known to have serious end point distortion, only partly alleviated by lagging the time series. 

This work just represents a small one-off contribution to Prof. Murtagh's interesting work based on 'a-trous' wavelets (2001).

Algorithms

This Excel utility calculates wavelet classes using one of the following algorithms:

  •     A-Trous
  •     Time-based A-Trous
  •     Redundant Haar
  •     Denoised Redundant Haar (multiscale entropy filtering)

These algorithms all originate from Prof F.Murtagh's research and software:   MultiScale Transform V2.  See http://www.multiresolution.com for a more comprehensive description.  It seems however that the A-Trous wavelet utility has been replaced by MR/Finance software, more comprehensive, and is no longer free of charge... The latest document (Sept 2001) is available on this site. Beware it can give headaches to traders only moderately inclined towards maths.

Our utility is functionally identical, but has been recoded for ease of use and performance (10 to 20 times faster).

It installs exactly like any MS Excel add-in.  Once installed, a new small icon appears on the menu bar.  Clicking the icon launches the Wavelet program.

Please send us your successful implementations of these wavelets in neural nets predictions.

Nota Bene: 

It is a free UNSUPPORTED download.  Source code available at a small fee (c.f. Sales page for price).
MultiResolution now offers a far more comprehensive software.  It must be understood that this work may there be dating a bit now, and may even prove to be inadequate or incorrect.  We are NOT wavelet specialists, and have not pursued the study of this kind of wavelet any further.

Wavelets have that annoying appearance of looking easy to use, but the learning curve can be pretty steep and results often disappointing at first.  

So, here are a few words of advice:
0.    Use Redundant Haar preferably;
1.    Detrend your data using %chg in price or sample z-score;
2.    Use enough bands to capture longer underlying trends (check size of the residual as a gauge for quality of decomposition);
3.    Use several bands in composite indicators to build great filters;
4.    Use band reversals, band slopes, %chg in slope as inputs in your neural nets;
5.    This is a great non linear tool, but still not a holy grail.   Still searching...


Download

Click here to reach the download page (Excel Add-In utility + samples).   Samples have been updated (April 2005)


Source Code

The source code can be purchased.  Price and details on our Sales page.  

Please contact us at sales@foretrade.com for details you may need.


Wavelet Links

For more theoretical details on the wavelet utility available on this site, you should obviously visit Prof. Murtagh's web site : http://www.multiresolution.com

Other interesting wavelet sites:

http://www.public.iastate.edu/~rpolikar/WAVELETS/WTtutorial.html (An excellent tutorial!!! Would almost make wavelets easy to understand!) 

Amara    (An excellent starting point and probably one of the best sites about wavelets)

The Wavelet Digest    (more advanced).

MathSoft Wavelets (excellent collection, like everything from MathSoft, but stick to the introduction level at the top of the page to avoid serious headaches)

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Page last modified: May 08, 2008
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