How to test if a time series is a white noise?

How to test if a time series x(t) (t=1,2...n) is a white noise?

x(t) does not have to be Gaussian. kstest() will not work. autocorr(X) only test auto-correlation; it does not show the mean at each t is zero.

Thanks

Answer 1

[Azzi Abdelmalek]

At each time t you have one value, the mean of this value is not supposed to be 0. You should calculate the mean of [x(1) x(2) ...]

[silicon]

According to the definition of white noise, X(t) for each t is a a random variable with 0 mean. So we have n random variables here. We should not calculate mean of [x(1) x(2) ...]

Answer 2

[Youssef Khmou]

white noise i.e flat power spectral density .

 % time serie X
 F=abs(fft(X)); 
 plot(F(1:end/2));    % shape?