4.8  White Noise, Moving-Average and
Autoregressive Processes

In this section, we consider several models, which are commonly used for specifying stationary conditionally homoskedastic processes.

4.8.1 White Noise Processes

A stochastic process

[4.50]

is said to be white noise if unconditional expectations satisfy

[4.51]

[4.52]

for some constant covariance matrix Σ. Condition [4.52] does not require that the ^tW be independent. If we assume they are, the process is called independent white noise. If we further assume the ^tW are joint normal, it is called Gaussian white noise.4 A realization of a univariate Gaussian white noise with variance 1 is graphed in Exhibit 4.10.

Exhibit 4.10: A realization of a univariate Gaussian white noise with variance 1.