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Thread: Time Series

  1. #1
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    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[$\displaystyle Z_0$] = ????
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    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 $\displaystyle \sigma^2$
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  4. #4
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    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.
    Last edited by bob000; Oct 23rd 2010 at 08:56 AM.
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