Properties of a White Noise Process

Before considering the different types of models mentioned above, it is instructive to first examine a white noise signal. A white noise signal is defined as 

The result follows from the fact that the signal values are independent of each other. This implies that for two values e, and e, t 7 0, the expected value will be zero. This is a very useful property of a white noise signal. The autocorrelation will then be 0 for all ITI 0 and 1 for t = 0. This implies that a white noise signal will have a single peak on a autocorrelation plot at t = 0. All other values will be zero. A pure, white noise signal is always invertible and causal. 

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