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stable_test(2) Scilab Function stable_test(2)
NAME
stable_test - stable law conformicy test
Author: Lotfi Belkacem
This routine tests the stability property of a signal.
Usage
[param,sd_param]=stable_test(maxr,data)
Input parameters
o maxr : integer positive scalar. maximum resolution witch depend on
the size of the sample.
o data : real vector [size,1] corresponding to the data sample (incre-
ments of the signal).
Output parameters
o param : real matrix [maxr,4] corresponding to the four estimated
parameters of the fited stable law at each level of resolution.
param(i,:), for i=1, ...maxr, gives respectively
alpha(characteristic exponent), beta (skewness parameter), mu (loca-
tion parameter), gamma (scale parameter) estimated at the resolution
i.
o sd_param : real matrix [maxr,4] corresponding to the estimated stan-
dard deviations of the four previous parameters at each level of
resolution. sd_param(i,:), for i=1, ...maxr, gives respectively
standard deviation of alpha, beta, mu and gamma estimated at the
resolution i.
Description
The stability test consists on estimating parameters of a fited alpha-
satble law at different level of resolution. the variable is said to be
stable if the charateristic exponent alpha remains approximatively constant
at different resolution, and the scale parameter follows a scaling law with
exponent (1/alpha)-1. .SH Example under scilab type:
[proc1_5,inc1_5]=sim_stable(1.5,0,0,1,20000);
[param,sd_param]=stable_test(7,inc1_5); alpha=param(:,1); m=(1:7)';
lnm=log(m); plot2d(m,alpha,1,'111','alpha',[1,0,7,2]); gamma=param(:,4);
lngamma=log(gamma); plot(lnm,lngamma); [a,b,sig]=reglin(lnm',lngamma');
slope=a th_slope=1/1.5-1
o we generate a standard 1.5-stable motion and its increments.
o we test the stability property of the previous simutated 1.5-stable
random variable "inc1_5" at 7 resolutions.
o we list estimated alpha at different scales.
o we visualize the stability of the shape parameter alpha.
o we list estimated gamma at different scales.
o we visualize the scaling law of the scale parameter gamma with a
log-log plot in the space (scale,scale parameter).
o we compute the slope "a" of the fited line which will be compared
to (1/alpha-1).
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