Question

For each of the following ARMA models, find the roots of the AR and MA polynomials, and identify the values of p and q for which they are ARMA(p,q). Remember to cancel out the common factors of AR and MA polynomials when determining p and q. Assume that {at}t?0 is a zero-mean unit variance white noise sequence. • rt + 0.81rt-2 = at + 1/3at-1. • rt - rt-1 = at - 1/2at-1 - 1/2at-2. • rt - 3rt-1 = at + 2at-1 - 8at-2. • rt - 2rt-1 + 2rt-2 = at - 8/9at-1. • rt - 4rt-2 = at - at-1 + 1/2at-2. • rt - 9/4rt-1 - 9/4rt-2 = at.

          For each of the following ARMA models, find the roots of the AR and MA polynomials, and identify the values of p and q for which they are ARMA(p,q). Remember to cancel out the common factors of AR and MA polynomials when determining p and q. Assume that {at}t?0 is a zero-mean unit variance white noise sequence.

• rt + 0.81rt-2 = at + 1/3at-1.
• rt - rt-1 = at - 1/2at-1 - 1/2at-2.
• rt - 3rt-1 = at + 2at-1 - 8at-2.
• rt - 2rt-1 + 2rt-2 = at - 8/9at-1.
• rt - 4rt-2 = at - at-1 + 1/2at-2.
• rt - 9/4rt-1 - 9/4rt-2 = at.

For each of the following ARMA models, find the roots of the AR and MA polynomials, and identify the values of p and q for which they are ARMA(p,q). Remember to cancel out the common factors of AR and MA polynomials when determining p and q. Assume that att?0 is a zero-mean unit variance white noise sequence.

• rt + 0.81rt-2 = at + 1/3at-1.
• rt - rt-1 = at - 1/2at-1 - 1/2at-2.
• rt - 3rt-1 = at + 2at-1 - 8at-2.
• rt - 2rt-1 + 2rt-2 = at - 8/9at-1.
• rt - 4rt-2 = at - at-1 + 1/2at-2.
• rt - 9/4rt-1 - 9/4rt-2 = at.

Added by Kristi M.

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