Question

2. Consider an ARM A(2,2) model h" ф.xt-1-фг%2 :: at + at-NI 1at-1 + 20.-2, a. Under what condition, the above ARMA(2,2) model is causal/stationary. b. Under what condition, the above ARMA(2,2) model is invertible. State the reason for us to consider an invertible ARMA model. Suppose that xt is causal, i.e. C. Calculate , j = 1,2,3,4,5,6. d. Suppose that x is invertible, i.e. Calculate nj, j-1,2,3,4,5,6.

Answer 1

Equating the cofficient of zej 0,, 2 we seb 2. Given thab ASANA 22 madel wherc Underthe condition Simlanly we can abtaia lpiまi 上hat d), suppose that at ts invest, ble le at: Xt.Σ〒/tǐ ARMA (7.2) prores con he wten ers ) Wa canP Thi sE th T,Z that satishes in Por zl b) Unde what condition the obore ARMAC22 madel inver bible State the reason Per n ARMA Condition Asumethat Poly nomlal 9rB)& r have no Common zeos Th Proress EXESi inve tible ff the zeos the MA Polynomial e(8) lie outside tho unit ircle Suppose thoi is caura ARMA (2,? Process can be wrilien a