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Estimation with a log-likelihood function

  1. Feb 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Hi, I am trying to solve a time series problem but I am stuck with a function I am not used to work with. I have a basic model AR(1) where e(t) has mean 0 and variance σ^2. The issue is that (e)t follows the density function attached to the post and it's causing me issues because of the gamma function with the (1/L) after. Does anyone know how I need to handle that part of the function to build my log likelihood function for (d,B,σ^2) ? L=Lambda (is a known parameter), G=gamma function, o is sigma


    2. Relevant equations

    y(t)=d +B(yt-1)+e(t) model



    3. The attempt at a solution

    What I have tried so far has let me with the following:

    -2/3 ln 2L - ln G(1/L) - Sum(t=2, T) (yt-d-B(yt-1))^L/(2o^2)^(1/2) - (y1-d/(1-B))^L / (2o^2/(1-B^2))^(1/2)


    Is this way of handling the density function with the Gamma correct (basically ignoring it as it goes away after the derivatives)? If not could anyone shed some light on the way I should approach this to solve it?

    Thanks a lot.
     

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    Last edited: Feb 4, 2012
  2. jcsd
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