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Math Help - Time Series

  1. #1
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    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] = ????
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    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
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  4. #4
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    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.
    Last edited by bob000; October 23rd 2010 at 08:56 AM.
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