Suppose $w_{t}$ is a normal white noise process. Is $z_{t} = w_{t}*w_{t-1}$ stationary?
Is my reasoning correct?
$Ew_{t}w_{t-1}w_{t+h}w_{t+h-1} = 0 $ for all $h$ implying that the series is stationary?
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Reading this, one wonders which definition of "stationary" you are using. – Did May 01 '13 at 19:41
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I am using the weakly stationary definition. The mean and covariance are not function of time. – phil12 May 01 '13 at 19:43
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Then to check that $E(z_t)=E(z_tz_s)=0$ for every $t\ne s$ and that $E(z_t^2)=1$ for every $t$ seems rather straightforward, no? – Did May 01 '13 at 19:45