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White Noise Process


Definition: A white noise process is a random process of random variables that are uncorrelated, have mean zero, and a finite variance (which is denoted s2 below).

Formally, et is a white noise process if E(et) = 0, E(et2) = s2, and E(etej) = 0 for t not equal to j, where all those expectations are taken prior to times t and j.

A common, slightly stronger condition is that they are independent from one another; this is an "independent white noise process."

Often one assumes a normal distribution for the variables, in which case the distribution was completely specified by the mean and variance; these are "normally distributed" or "Gaussian" white noise processes.


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