iirgrpdelay no impact on the waveform

Hello, I am trying to simulate the impact that a filter's group delay response could have on a waveform. I use the following code: clear all N=10;

F=[0:0.01:1];

b=a;

numel(b(1:101))

b=abs(b(1:101))

numel(b)

numel(F)

x=bocf2;

edges=[0 1]

[num,den]=iirgrpdelay(N,F,edges,abs(b));

y = filter(num,den,x)

subplot(211)

plot(x); title('Input Signal');

grid on; ylabel('Amplitude');

subplot(212);

plot(y); title('Output Signal'); grid on;

xlabel('Samples'); ylabel('Amplitude');

figure

plot(xcorr(x))

figure

plot(xcorr(y))

The bocf2 is a 2 khz bandwidth waveform,which i pass through the filter by applying that group delay introduced by a. Can you please explain me why the correlation of the input is the same with the one of the output of the filter while the delay has been applied?