If you'll look up for the definition of a (discrete) white noise process on the web, you'll find some sources that say:
"white noise is defined by zero mean, finite and constant variance, zero autocorrelation"
and roughly the same amount of them that say:
"white noise is defined by zero mean, finite variance, zero autocorrelation".
In the latter (e.g. the Wikipedia page), "white noise" encompasses also the case of heteroskedastic white noise – where the variance isn't constant. Obviously, stationarity is dropped.
Which of these two is "the" standard definition? Am I missing something?
Note: I submitted the same question in math.stackexchange. Whenever I get an answer, I'll delete the other one.
Best Answer
There is no common definition of white noise.
You have two definitions. And there exists more definitions. For example, white noise is a stationary stochastic process with constant spectral density (and thus infinite variance).
https://www.encyclopediaofmath.org/index.php/White_noise