Question

{Zt} is a Gaussian White Noise in time series. Yt = Zt^2. Can we conclude Yt as a non-Gaussian White Noise distribution by the definition of White Noise? Why?

Answer 1

White Noise:

A period arrangement rt is known as a repetitive sound {rt} is a succession of autonomous and indistinguishably circulated irregular factors with limited mean and fluctuation. Specifically, if rt is ordinarily dispersed with mean zero and fluctuation σ2, the arrangement is known as a Gaussian background noise.

The conduct of test autocorrelations of the esteem weighted record returns shows that for some advantage returns it is important to demonstrate the sequential reliance before further examination can be made.

where μ is the mean of rt, ψ0 = 1, and {at} is a grouping of iid arbitrary factors with mean zero and a very much characterized conveyance (i.e., {at} is a background noise).

Gaussian white noise in time series (Zt):

A period arrangement is repetitive sound the factors are independent and identically  circulated with a mean of zero. ... On the off chance that the factors in the arrangement are drawn from a Gaussian disribution , the arrangement is called Gaussian repetitive sound.

Yt=Zt^2.Therfore yt is non Gaussian white noise distribution by the definition of white noise.