stationarity of this time series

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

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

But the covariance:

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

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

Re: stationarity of this time series

Hello,

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

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