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Find variance change points


[PTS_OPT,KOPT,T_EST] = wvarchg(Y,K,D)


[PTS_OPT,KOPT,T_EST] = wvarchg(Y,K,D) computes estimated variance change points for the signal Y for j change points, with j = 0, 1, 2, ... , K.

Integer D is the minimum delay between two change points.

Integer KOPT is the proposed number of change points (0 ≤ KOPTK). The vector PTS_OPT contains the corresponding change points.

For 1 k K, T_EST(k+1,1:k) contains the k instants of the variance change points and then, if KOPT > 0, PTS_OPT = T_EST(KOPT+1,1:KOPT) else PTS_OPT = [].

K and D must be integers such that 1 < K << length(Y) and 1 ≤ D << length(Y).

The signal Y should be zero mean.

wvarchg(Y,K) is equivalent to wvarchg(Y,K,10).

wvarchg(Y) is equivalent to wvarchg(Y,6,10).


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Detect Variance Change Points

Add two variance change points to the blocks signal. Detect the variance change points using wvarchg.

Load the blocks signal. Add white noise with two variance change points located at index 180 and 600.

x = wnoise(1,10);
rng default;
bb = 1.5*randn(1,length(x));
cp1 = 180; cp2 = 600;
x = x + [bb(1:cp1),bb(cp1+1:cp2)/4,bb(cp2+1:end)];

Obtain the level-1 wavelet coefficients. Replace the top 2% of values with the mean value of the wavelet coefficients to remove all signal.

wname = 'db3'; lev = 1;
[c,l] = wavedec(x,lev,wname);
det = wrcoef('d',c,l,wname,1);
y = sort(abs(det));
v2p100 = y(fix(length(y)*0.98));
ind = find(abs(det)>v2p100);
det(ind) = mean(det);

Estimate the variance change points using the wavelet coefficients.

[pts_Opt,kopt,t_est] = wvarchg(det,5);
sprintf('The estimated change points are %d and %d\n',pts_Opt)


Lavielle, M. (1999), "Detection of multiple changes in a sequence of dependent variables," Stoch. Proc. and their Applications, 83, 2, pp. 79–102.

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