This is a collection of matlab functions for generating so-called
`surrogate time series'.  They are basically realisations of a given
`original' time series (first input argument) under the assumption of a
certain null hypothesis, H0.  Traditionally, they are used for testing
the presence of nonlinearities in time series.  A *very* interesting
overview of surrogate data generation methods is:

Schreiber, T. and Schmitz, A. (2000), Surrogate Time Series, Physica D,
142, 346--382.

which can be downloaded from:
http://www.mpipks-dresden.mpg.de/~schreibe/myrefs/myrefs.html

The basic idea is to compute a test statistic, t, for the original time
series, X, and on a number of surrogate time series, Xs, yielding t_o
and {t_s}.  The null hypothesis, H0, is rejected if t_0 is significantly
different from {t_s}, e.g. using a (left-, right- or two-tailed)
rank-based test.

These functions are implementations of different surrogate data generation
methods (described in Schreiber and Schmitz, 2000).

generate_randperm.m
generate_AR.m
generate_AAFT.m
generate_FT.m
generate_iAAFT.m
generate_iAAFTn.m
generate_anneal.m	Example of a simulated annealing approach
end2end.m		Endpoint matching procedure (alleviates bias in
			surrogates;  see Schreiber and Schmitz, 2000)

A quick and very sketchy tutorial can be found in quick_tutorial.txt

A number of interesting links wrt signal nonlinearity detection:
http://www.physik3.gwdg.de/tstool/
http://www.theochem.uni-frankfurt.de/~hegger/
http://nis-www.lanl.gov/~jt/Papers/
http://www.macalester.edu/~kaplan/
http://www.mpipks-dresden.mpg.de/~tisean/TISEAN_2.1/index.html
http://134.58.34.50/temu

Maybe the DVV toolbox could be worth looking at in the context of 
signal nonlinearity testing:
http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=3264

I have added a number of surrogate data generation methods for other
applications.  For those interested, I have added the refs to the papers
where they are described/used.

generate_corr_pair.m
	Gautama, T. and Van Hulle, M.M. (2003), Surrogate-based Test for
	Granger Causality, Proceedings IEEE Neural Network for Signal
	Processing Workshop 2003, Toulouse, France, 799--808.
	http://134.58.34.50/temu/nnsp03.ps.gz
These surrogates retain the empirical distribution of the original
data, and the instantaneous correlation to a given reference data set.
They can be used for checking if there are relations between data sets
that cannot be explained from simple correlations.

generate_ciAAFT.m
	Gautama, T., Mandic, D.P. and Van Hulle, M.M. (2003),
	Non-parametric Test for Detecting the Complex-Valued Nature
	of Time Series, Proceedings of Knowledge-Based Intelligent
	Information and Engineering Systems (KES 2003), Part I,
	1364--1371.
	http://134.58.34.50/temu/kes03.ps.gz
This is a complex-valued extension of the iAAFT method.

generate_stat_boot.m
	Politis, D.N. and Romano, J.P. (1994), The Stationary Bootstrap,
	J. Am.	Stat. Assoc., 89 (428), 371--384.
	Diks, C. and DeGoede, J. (2001), A General Nonparametric Bootstrap
	Test for Granger Causality, in: "Global Analysis of Dynamical
	Systems", Broer, H. and Krauskopf, B. and Vegter, G. (eds),
	pp. 391--403.
The null hypothesis underlying this type of surrogate is that the original
time series is stationary.  Basically, it generates a sequence of time
segments of random length, taken from the original time series.


A number of data generation functions:
generate_ar_signal.m	Generate a linear (AR) signal
generate_henon.m	Generate a chaotic Henon map

comp_rev.m		Compute the asymmetry due to time reversal
				(one possible measure for nonlinearity)
ranktest.m		Rank-testing procedure for statistical testing