1. ## Time Series

I have to work out whether its weakly stationary or not

Xt = b$\displaystyle Z_0$ where b is a constant.

I know i have to work out that the mean first and make it finite and not dependent on t.

What does E[$\displaystyle Z_0$] = ????

2. Without knowing what $\displaystyle Z_0$ is or knowing what the distribution of x is, if "$\displaystyle x_t= bZ_0$ is the definition of $\displaystyle Z_0$, I don't see how anyone can answer that question.

3. Originally Posted by HallsofIvy
Without knowing what $\displaystyle Z_0$ is or knowing what the distribution of x is, if "$\displaystyle x_t= bZ_0$ is the definition of $\displaystyle Z_0$, I don't see how anyone can answer that question.
$\displaystyle Z_t$ is assumed to be generated by a zero mean independent identically distributed noise process with a variance $\displaystyle \sigma^2$

4. Do you by any chance mean

$\displaystyle X_t$= b$\displaystyle X_t_-_1$ + $\displaystyle e_t$ where e is a zero mean independent identically distributed noise process with a variance?

If so $\displaystyle X_t_+_n$= $\displaystyle b^n$$\displaystyle X_t$ + a bunch of mean zero terms with variance equal to var(e)/(1-b^2). Since b^n converges to zero the series is stationary.

As you have it written $\displaystyle X_t$ is generated by repeated draws from an iid distribution and isnt really a time series.