I read that one condition for weak stationarity is that a series needs to have a constant mean.

My (rather short) question: Does weak stationarity require the variance to be constant as well or is having a finite variance sufficient (or does one imply the other)?

This distinction not seem to be treated in a uniform manner in the literature I encountered. (However, maybe it is me who overlooks something obvious)

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#### Best Answer

Yes, weak stationarity requires both constant variance and constant mean (over time). To quote from wikipedia: *A wide-sense stationary random processes only require that 1st moment (i.e. the mean) and autocovariance do not vary with respect to time.*

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