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Math Help - Time Series Help!

  1. #1
    Member
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    Time Series Help!

    Hey guys, first time taking a time series class, need some help!
    Let { Z_{t}} be an IID sequence with mean 0 and variance \sigma^2. (I think this is White Noise)
    Let { Y_{t}} be a stationary sequence with a covariance function \gamma_{y}(k). Then it says assume Z_{t} and Y_{t} are independent of each other.
    Define  X_{t}=Z_{t}Y_{t}.
    Verify that for k ≥ 1 we have Cov( X_{t}, X_{t+k}) = 0 and Cov( X^2_{t}, X^2_{t+k}) ≠ 0, that is { X_{t}} is a white noise but not IID.


    So Im not sure how to define X_{t}? Its the product of white noise ( Z_{t}) and some stationary sequence ( Y_{t})?
    Any help would be appreciated.
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  2. #2
    MHF Contributor
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    Re: Time Series Help!

    Hey calculuskid1.

    Doesn't the question already give you the definition (i.e. Xt = Zt*Yt)?
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