# Math Help - Time Series Help!

1. ## Time Series Help!

Hey guys, first time taking a time series class, need some help!
Let { $Z_{t}$} be an IID sequence with mean 0 and variance $\sigma^2$. (I think this is White Noise)
Let { $Y_{t}$} be a stationary sequence with a covariance function $\gamma_{y}(k)$. Then it says assume $Z_{t}$ and $Y_{t}$ are independent of each other.
Define $X_{t}=Z_{t}Y_{t}$.
Verify that for k ≥ 1 we have Cov( $X_{t}$, $X_{t+k}$) = 0 and Cov( $X^2_{t}$, $X^2_{t+k}$) ≠ 0, that is { $X_{t}$} is a white noise but not IID.

So Im not sure how to define $X_{t}$? Its the product of white noise ( $Z_{t}$) and some stationary sequence ( $Y_{t}$)?
Any help would be appreciated.

2. ## Re: Time Series Help!

Hey calculuskid1.

Doesn't the question already give you the definition (i.e. Xt = Zt*Yt)?