Linear Processes and Stationarity

hello,

a linear process (e.g. ARMA)

y_t = H(B)\epsilon_t
B -> backward shift operator

with transfer function H(z^{-1}) is said to be 'stationary' if the ROC
includes |z| >= 1.

i can see how this requirement implies causality and stability of the linear
response - but i don't understand the relationship between stationarity (i'm
assume this means wide sense stationary?) and the convergence of the
z-tranform of the transfer function. any pointers would be appreciated.

thanks,
-g





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