Time Series

**adam_leeds** · October 23rd 2010, 02:38 AM

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[ $Z_0$ ] = ????

**HallsofIvy** · October 23rd 2010, 07:19 AM

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.

**adam_leeds** · October 23rd 2010, 08:15 AM

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 $\sigma^2$

**bob000** · October 23rd 2010, 08:39 AM

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.

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