Question

7. What are the model assumptions of the following process and the corresponding model param- eters? Is the following model stationary? Is it invertible? Justify your answers.

Xt + 1.5Xt−1 = Wt − 0.5Wt−1 + 0.07Wt−2

where Wt is a sequence of i.i.d. normal random variables with mean zero and variance 1.

Answer 1

It appears to be an ARMA(1,2) model as x terms depends on previous values of period one. So that gives Auto regressive of order (1) and errors terms goes upto period 2 back in time so it gives moving average of order (2) hence combined model is ARMA(1,2).