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AR (Autoregressive) Model

  1. Dec 13, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider the AR(2) model (1 - x1*B - x2*B^2)Xt = εt. Show that Xt is a stationary process if and only if the following inequalities are satisfied:

    x1+ x2 < 1
    x2-x1< 1
    |x2| < 1

    3. The attempt at a solution
    1 - x1*B - x2*B^2 = 0
    |B| > 1 so then use quadratic formula to get B = (-x1 +- sqrt(x1^2 + 4x2)) / (2x2)

    Do I need to consider all 6 cases (x2 > 0, x2=0, x2 < 0, x1 > 0, x1=0, x1<0)?

    I think at some point I have to mess with complex roots.

    Is there an easier way of looking at this problem or do I have to go through each case?
  2. jcsd
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