## WOLD THEOREM

It is the theorem that allow to represent a weakly stationary with mean zero stochastic process (Xt), as the sum of the products of the parameter φ (sequence of real numbers) by the factor ε (sequence of independent identically distributed random variables, with zero mean and variance σ2):

So that is:

and ensure that the process is stationary must be verified both the mean and variance of the following reports:

from which it follows:

but also those of the autocorrelation and auto-covariance:

so it is:

Editor: Giuliano DI TOMMASO