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Time series, normal distribution?

  1. Feb 19, 2012 #1
    1. The problem statement, all variables and given/known data

    If I have a time series model

    x_1 = my + epsilon_1
    x_i = my + a(x_{i-1} - my) + epsilon_i

    epsilon_i are iid standard normal.

    Can I then say that
    y = a_1 x_1+a_2 x_2 + .... a_n x_n

    is multi normal?



    3. The attempt at a solution

    All the x-es are normal since they are built up of previous epsilons thich are independent and normal.

    But the x-es are not independent so can I then say that a linear combination of them is normal
     
  2. jcsd
  3. Feb 20, 2012 #2
    absolutely, any linear combinations of joint Gaussian plus whatever constant is still joint Gaussian (in your case, iid Gaussian is a special joint Gaussian)
     
  4. Feb 21, 2012 #3
    Thanks for the help.
     
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