Release Notes for S+Wavelets Version 2.0 (December 2003)


S+Wavelets Version 2.0 contains an updated version of S+Wavelets
Version 1.0.

This file contains the following information:

SUPPORTED PLATFORMS AND SYSTEM REQUIREMENTS 
WINDOWS REQUIREMENTS
SOLARIS REQUIREMENTS 
ENHANCEMENTS 
NOTES AND KNOWN ISSUES
RUNNING S+WAVELETS
USER'S GUIDE PDF
CONTACT INFORMATION FOR FEEDBACK


SUPPORTED PLATFORMS AND SYSTEM REQUIREMENTS

S+Wavelets Version 2.0 requires S-Plus 6.1 Release 1 or later on
Microsoft Windows and Solaris platforms.


WINDOWS REQUIREMENTS

S+Wavelets Version 2.0 for Windows is supported on the following:

   Windows NT 4.0 (Service Pack 6), Windows 2000, Windows 2003 Server,
   and Windows XP Professional.

The minimum recommended system configuration is the same as S+ 6.x for
Windows: Pentium II/233 with 96MB of RAM. You must have at least 15MB
of free disk space for the typical installation.


SOLARIS REQUIREMENTS

S+Wavelets Version 2.0 for Solaris is supported on the following:

	Solaris 2.8 and 2.9


ENHANCEMENTS

The new methodology implemented in S+Wavelets 2.0 stems almost entirely
from Don Percival’s book entitled, Wavelet Methods for Time Series
Analysis, co-authored by Andrew Walden and published by Cambridge
University Press in 2001. A summary of the relevant new methodology is as follows:

1. New wavelet transforms

The new transforms include the (i) convolution style DWT, (ii) maximal overlap discrete wavelet transform (MODWT), (iii) convolution style discrete wavelet packet transform (DWPT), and (iv) maximal overlap discrete wavelet packet transform (MODWPT). These differ from those in S+Wavelets 1.x in that they (1)  are based on convolution style filtering, (2) only use periodic boundary conditions (making them energy conservative and usable for wavelet variance estimation), and (3) are designed so that the boundary
coefficients (those subject to circular filter operations) are easily
identifiable, making them useful for certain wavelet-based statistics.
We have also implemented the Dual Tree Wavelet Transform (DTWT) in both
1-D and 2-D. The DTWT has the advantage of being approximately
shift-invariant without only a two-fold degeneracy. The corresponding
multi-resolution decompositions and approximations are also coded in
S+Wavelets 2.0.

2. Wavelet variance-covariance estimators

If you integrate (over frequency) the spectral density function (SDF),
you obtain the variance. The wavelet variance is a regularization of
the SDF in that it represents the variance of the process on a
scale-by-scale basis (each scale is associated with a particular octave
band of frequencies). Both biased and unbiased versions of the MODWT
and DWT variance estimators have been implemented. A homogeneity of variance test is also implemented and can be used for detecting signal nonstationarities.

3. Fractionally Differenced (FD) Process parameter estimators

If the SDF follows a power law, then it is known as a colored noise
process (e.g., white noise, pink or 1/f noise, random walk or red
noise, etc.).  The level of the SDF and the log-log slope (alpha) of
the SDF are the two parameters that govern the model. Many real-world
processes exhibit colored noise behavior, whose alpha fluctuates as a
function of time. Of all the power law models, the so-called fractionally differenced (FD) model is arguably the best (no restriction on alpha, no continuity problems at pink noise border, simple mathematical model). In S+Wavelets, we have implemented wavelet-based estimators of FD model parameters, ranging from instantaneous to block estimators. We also have two types:
weighted least squares and maximum likelihood estimators. This
technology has been used successfully on the analysis of aerothermal
turbulence data. But it may also have a place in the finance community,
where (possibly short term) SDF power law behavior exists. Finally, functionality to produce time-varying FD simulations is also implemented in the new version of S+Wavelets.

NOTES AND KNOWN ISSUES

cpt.2d: The function cpt.2d fails in certain circumstances. In particular, the example in the help file fails:

   xx <- phone-mean(phone) 
   par(mfrow=c(1,2)) 
   image(xx) 
   bb2 <- crystal.names("block.dct.2d", 2) 
   cc2 <- cpt.2d(xx, crystal.names=bb2, taper="poly2") 

with the following error message:

   Problem in cpt.2d(xx, crystal.names = bb2, taper = "poly2"): Object "rdict" not found


RUNNING S+WAVELETS

From within S-PLUS, at the command line, enter:

> module(wavelets)

In S-PLUS for Windows, you can also load S+Wavelets by choosing File >
Load Module > wavelets from the menus.


USER's GUIDE PDF

The Wavelets 2 User's Guide is available in pdf form. The file is called S+Wavelets2.pdf, and you can locate it in your SHOME/modules/wavelets directory.


CONTACT INFORMATION FOR FEEDBACK

Please feel free to contact us with questions or feedback about this
release. Send all questions and general comments to:

	bugs@insightful.com

We are very interested in receiving your comments and suggestions for
improving S+Wavelets.