stationarity of this time series

**noob mathematician** · August 29th 2011, 06:57 AM

Given that $Y_t=(-1)^tZ$ where $Z$ is a rv with mean 0 and variance 1. Is this a stationary series?

The expected value, $E[Y_t]=0$

But the covariance:

$COV(Y_t,Y_{t+h})=E[Y_tY_{t+h}]=E[(-1)^tZ(-1)^{t+h}Z]=E[(-1)^{2t+h}Z^2]=(-1)^{2t+h}E[Z^2]=(-1)^{2t+h}$

This is dependent on t for all h and therefore am i right to say that it is non-stationary?

**Moo** · August 30th 2011, 08:10 AM

Hello,

And what is $(-1)^{2t}$ ?

It is stationary because $a^{bc}=(a^b)^c$ !

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