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Having trouble understanding sources of hetroscedasticity

  1. May 13, 2012 #1
    Hey. Iam trying to understand how specification of the equation can lead to hetroscedasticity. This is stright out of my notes.

    Yt=B1+B2x2t+B3x3t+......+BkXkt+[itex]\gamma[/itex][itex]\varpi+[/itex]ε[itex]^{}_{t}[/itex]


    Yt=B1+B2x2t+B3x3t+......+Bkxkt+ε[itex]^{*}_{t}[/itex]

    where
    ε[itex]^{*}_{t}[/itex] = εt + [itex]\gamma[/itex][itex]\varpi[/itex]t

    Since Var(εt) = [itex]\sigma[/itex][itex]^{2}_{ε}+[/itex][itex]\gamma[/itex][itex]^{}_{t}[/itex]var([itex]\varpi[/itex]t)

    I dont understand the variance part. I know that the variance of any epsilon is [itex]\sigma[/itex]2, but why does the γt go outside the variance operator? I know it's a constant so why isn't it γ2?
     
  2. jcsd
  3. May 14, 2012 #2
    If γ is a constant the it's a typo and γ should be squared when outside the variance.

    This seems a time series, so one to way to introduce heterocedasticity in this model is by increasing γt over time, I am assuming ϖ is a random variable with the same behavior over time (it's not clear in your formulation since sometimes they both have the t subscript at the end but not in the beginning).
     
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