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The normwhn.test package in R has a function to test if data is white noise. The documentation of the function states the following :

Performs an Univariate Test for White Noise. The null is white noise rather than "strict" white noise, thus permitting weak dependence in the higher moments of the variable

What is meant by "strict" white noise ? And what does it mean to permit weak dependence in higher moments ?

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By definition, 'white noise' is serially uncorrelated. It is like hitting piano keys at random; note n+1 cannot at all be predicted by note n. This is distinguished from brown noise and pink noise, both of which have some serial correlation, or dependence, albeit to different extents. To answer your question, 'strict white noise' assume essentially 0 serial correlation, whereas the alternative 'white noise' in your description would allow for the fact that natural phenomena often times present with some degree of correlation even when remaining memory free.

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