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