TS Module 7: stationary mixed processes HW
(The attached PDF file has better formatting.)
Homework assignment: mixed autoregressive moving average process
An ARMA(1,1) process has ó2 = 1, è1 = 0.4, and ö1 = 0.6.
A. What is the value of ã0?
B. What is the value of ã1?
C. What is the value of ñ1?
D. What is the value of ñ2?
I'm blanking, what is Filter Representation?
Also, I got the same answer as above for the first problem. As to the "crazy" amount of algebra, the formulae on page 78 (4.4.3-5) made this assignment take a couple minutes.
My understanding of filter representations is that it's used to estimate the variance of forecast. We can convert the φ parameters into an infinite series of θ parameters. This is helpful because the θ parameter only changes one period in the future. I'm anticipating that the final might ask, "What is the variance of the one period ahead forecast? Two? Three?"
There's a few practice problems in the Module 7 Stationary mixed processes that might be helpful in understanding the concepts.
[NEAS: Correct; the filter representation converts an autoregressive processes into a moving average model of infinite rank. This simplifies the formulas for the variance of forecasts because all the error terms are independent, whereas the observations are serially correlated.]