Time Series

• Oct 23rd 2010, 03:38 AM
Time Series
I have to work out whether its weakly stationary or not

Xt = b $Z_0$ 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[ $Z_0$] = ????
• Oct 23rd 2010, 08:19 AM
HallsofIvy
Without knowing what $Z_0$ is or knowing what the distribution of x is, if " $x_t= bZ_0$ is the definition of $Z_0$, I don't see how anyone can answer that question.
• Oct 23rd 2010, 09:15 AM
Quote:

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

$Z_t$ is assumed to be generated by a zero mean independent identically distributed noise process with a variance $\sigma^2$
• Oct 23rd 2010, 09:39 AM
bob000
Do you by any chance mean

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

If so $X_t_+_n$= $b^n$ $X_t$ + 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 $X_t$ is generated by repeated draws from an iid distribution and isnt really a time series.