General constrained randomization:
Standard nonlinearity test

The most important specific calling sequence is used to generate surrogates with the same autocorrelation function and the same distribution of the data. The corresponding null hypothesis is that the data have been generated by a stationary Gaussian linear stochastic process, rescaled by a static, monotonic, measurement function. For this purpose, usually AAFT surrogates or those iteratively generated by surrogates are used. The present alternative is more accurate and avoids the edge artefact through the use of the non-periodic autocorrelation function rather than the FFT. It is however much more CPU (and user) time intensive. See the paper for an introduction to general constrained randomization of time series.

randomize_auto_exp_random -D# [-W#]
     [-n# -u# -I# -o outfile -l# -x# -c# -V# -h
     -T# -a# -S# -s# -z# -C# -X xfile] file


-D number of lags for autocorrelation
-W type of average: 0=max(c), 1=|c|/lag, 2=(c/lag)**2, 3=max(c)/lag (default 0)
-n number of surrogates (default 1)
-u improvement factor before write (default 0.9 = if 10% better)
-I seed for random numbers (0)
-l maximal number of points to be processed (default all)
-x number of values to be skipped (0)
-c column to be read (1 or file,#)
-o output file name, just -o means file_rnd(_nnn)
-V verbosity level (0 = only fatal errors)
-h show usage message
-T initial temperature (default: automatic melting)
-a cooling factor (default automatic)
-S total steps before cooling (default 20000)
-s successful steps before cooling (default 2000)
-z minimal successful steps (default 200)
-C goal value of cost function (default zero)
-X file containing list of indices excluded from permutation

verbosity level (add what you want):

1 = input/output
2 = current value of cost function upon printable improvement
4 = cost mismatch
8 = temperature etc. at cooling
16 = verbose cost if improved
32 = verbose cost mismatch

Note: if neither -a nor -C are given, the annealing will keep starting over with slower cooling rates. This may be necessary if good guesses are not available but of course, multiple surrogates will have to be made by further separate calls.

Periodic autocorrelation

Note: There is an alternative call randomize_autop_exp_random with identical arguments that uses a periodically continued version of the autocorrelation function. This is usually not desired but I kept it for comparison with FFT based surrogate methods which implicitly assume such periodicity.

Usage example

Try also just running: gnuplot randomize.gnu in the examples directory. 

> randomize_auto_exp_random -o -D50 -T0.005 -a0.95 -C0.001 spike.dat

gnuplot> plot 'spike.dat'
gnuplot> plot 'spike.dat_rnd'

spike data

spike surrogate

Constrained Randomization * Table of Contents * TISEAN home