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Does the Absence of a Unit Root Imply Wide Sense Stationarity?
If you restrict inquiry to ARIMA processes alone, absence of a unit root implies stationarity. If you consider time series processes in general, absence of a unit root certainly does not imply ...
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Mean square convergence of a series of stationary random variables
For the answer above, you can assume without lose of generality that $\mu = E X_t = 0$, because if you define $X_t' = X_t- \mu$ (which has the same autocovariance function as $X_t$), then
\begin{align*...
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