Time series -Whitenoise



Hi Experts,

What is the best way of defining white noise process so it is intuitive and easy to understand?Please elaborate.

insights much appreciated.




A white noise process is a random process of random variables that are uncorrelated, have mean zero, and a finite variance. Formally, X(t)X(t) is a white noise process if

E(X(t))=0,E(X(t)2)=S2, and E(X(t)X(h))=0 for t≠h.
E(X(t))=0,E(X(t)2)=S2, and E(X(t)X(h))=0 for t≠h.

A slightly stronger condition is that they are independent of one another; this is an “independent white noise process.”

Hope this helps!



Let E(t) be the white noise and this can be represented as


with mean 0 and variance 1. The critical assumption is IID, that errors are identically and independently distributed.