MATLAB: Calculation of autocorrelation matrix

autocorrelation

I want to calculate autocorrelation matrix of a give sequence in matlab.

Which command I have to use ?

>> x=[-2 1 4 2 1 5 4 2 4]
>> z=autocorr(x)

I am getting auto correlated values in a vector form.

I want to calculate Rxx which is a matrix. Suppose if the length of the vector ix N I have to get N X N matrix.

I tried corrmtx( ) but not worked.

Please some one answer my question..

Best Answer

I don't have the econometrics toolbox, but from this:

http://en.wikipedia.org/wiki/Autocorrelation_matrix

it looks like you might be able to build it by using the vector and the TOEPLITZ function (or cousins).

Related Solutions

MATLAB: Autocorrelation Matrix from a vector

No, that is not correct. The way you are doing it is not giving the autocorrelation matrix. For one thing your matrix is not going to be Toeplitz.

For example:

    x = randn(10,1);
    rxx = x*x';

Note the above, rxx, is not Toeplitz.

But

[xc,lags] = xcorr(x,x,9,'biased');
r = xc(10:end);
rxx = toeplitz(r,conj(r)); % the conj() of course here is not needed

Now, rxx is Toeplitz and not that the autocorrelation matrix has full column rank.

rank(rxx)

Or you could do:

    X = fft(x,2^nextpow2(2*size(x,1)-1));
    R = ifft(abs(X).^2);
    m = length(x);
    R = R./m; % Biased autocorrelation estimate
    rxx = toeplitz(R(1:length(x)),conj(R(1:length(x))));

MATLAB: Isn’t the autocorrelation of rand a delta function

As described in detail here, http://en.wikipedia.org/wiki/Autocorrelation, there is more than one convention when calculating autocorrelation. In signal processing, autocorrelation of a sequence is often calculated without subtracting off the mean. As described in the documentation, this is indeed what XCORR does:

http://www.mathworks.com/help/signal/ref/xcorr.html

By default, xcorr computes raw correlations with no normalization.

If you generate the uniform random numbers with no bias (subtract 0.5), you will indeed get a result that looks like a delta function.

x=rand(1,100,1)-0.5; Rxx=xcorr(x); subplot(2,1,1); plot(Rxx); grid; title('Autocorrelation function of rand'); xlabel('lags'); ylabel('Autocorrelation');
x=randn(1,100,1); Rxx=xcorr(x); subplot(2,1,2); plot(Rxx); title('Autocorrelation function of randn'); xlabel('lags'); ylabel('Autocorrelation');

Best Answer

Related Solutions

MATLAB: Autocorrelation Matrix from a vector

MATLAB: Isn’t the autocorrelation of rand a delta function

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