All common tests for testing if a time series is white noise are based on common distribution assumptions from which inference is made that a process is white noise.

However, in the case for most time series the underlying distributions do not follow traditional distributions (gausian etc). For this reason I would like to know if any white noise tests exist which do not use preconcived distributions and observes main white noise assumptions (finite variance, serially uncorrelated ( independent / statinonary) and zero mean).

Using density spectrum as to see if the density plot produces a flat line through FFT is not possible as the series is non stationary.

  • $\begingroup$ The longer your FFT block, the more closely white noise resembles a flat line. Averaging multiple shorter FFTs of white noise will also approach a flat line. However, neither is sufficient as a test of true white noise since a chirp synchronized to the FFT block will also produce a flat line. $\endgroup$ – JRE Jan 7 '16 at 8:39
  • $\begingroup$ I could have sworn I read, and commented, on this question on stats.SE a few hours ago. $\endgroup$ – Dilip Sarwate Jan 7 '16 at 23:02
  • $\begingroup$ as it is an stats and also a signal procesing through in psting in bouth. $\endgroup$ – Barnaby Jan 8 '16 at 13:47

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