I cannot multiply, Multiple times I accidentalyy said .5T*T=T^2 and T is theta, the simplest mistakes are the dumbest, but it, thanks

Jeffry,

I don't think the answers you cited are correct. I believe the answer to A is 0.5, and the answer to B only has one root, which is 1. These can be easily found by using equation 7.1.5 to get phi, and then plugging everything into equation 7.1.6 and solving for theta using the quadratic formula.

I would still like help with the solution if anybody is taking the Summer 2011 course, I have come back and still cannot figure out my mistake.

ok, what am i doing wrong, i am looking at the solutions people used earlier, of 1.558 and .642.  I used equations 7.1.5 to get A that phi is .5 and 7.1.6, which I have not solved.  I would agree with the solutions listed if r1 was -.125 and phi was the same, however r1 is -.25.  Can anybody tell me what I am missing?

How come I only get theta = 1. one root? I check mulitple time. could not figure out what i did wrong.

TME

Did anyone actually find an invertible sol'n for theta?

Dave and Michelle, you are absolutely correct!  I got your answer also.

I agree with Michelle, and without giving my answer away, I got something for theta that wasn't less than 1, but at the same time, wasn't greater than 1.  And the part I'm agreeing with is that the two roots are equal.  Soooooooo.........

   -    Dave

In general, quadratic equations have two solutions (think of the +/- before the square root term in the numerator).

Page 79 describes how to test for invertability, but I didn't fully understand it.  Since equation 7.1.4 tells you to use the positive sign before the square root term for the MA(1) case, I guessed that we should use that for the ARMA(1,1) case as well.

By the way, the 2 roots I got were 1.558 (using the positive sign before the sqrt) and 0.642 (using the negative sign before the sqrt).

[NEAS: Use the solution whose absolute value is less than one. The textbook gives the rules; this homework assignment is an example. The textbook says to solve the quadratic equation and choose the root that is less than one in absolute value.]

NEAS:  How do we know which solution is invertible for an ARMA(1,1) model?  Page 151 states that a quadratic equation must be solved and only the invertible solution retained.  Unless I calculated the homework wrong, it only has one solution.  That said, I'm not sure how to proceed in cases with two solutions.

[NEAS: Generally, the solution with |theta| < 1.]