# hw5 - MA ∞ model(d Evaluate the ﬁrst three AR...

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AMS316 HW5 (Due Nov 30, 2011) 1. Following the procedure I have done in class, show that the ACFs of the ARMA (1 , 1) model, X t = αX t - 1 + Z t + βZ t - 1 , | α | < 1 , | β | < 1 , is given by ρ (1) = (1 + αβ )( α + β ) / ( 1 + β 2 + 2 αβ ) ρ ( k ) = αρ ( k - 1) ,k = 2 , 3 ,... 2. For the model (1 - B )(1 - 0 . 2 B ) X t = (1 - 0 . 5 B ) Z t : (a) Classify the model as an ARIMA ( p,d,q ) process(i.e. ﬁnd p,d,q). (b) Determine whether the process is stationary and invertible. (c) Evaluate the ﬁrst three MA coeﬃcients of the model when ex- pressed as
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Unformatted text preview: MA ( ∞ ) model. (d) Evaluate the ﬁrst three AR coeﬃcients of the model when ex-pressed as AR ( ∞ ) model. 3. Show that AR(2) process X t = X t-1 + cX t-2 + Z t is stationary provided-1 < c < 0. Find the autocorrelation function when c =-3 / 16. 4. Show that the AR (3)process X t = X t-1 + cX t-2-cX t-3 + Z t is non-stationary for all values of c. 1...
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## This note was uploaded on 02/28/2012 for the course AMS 316 taught by Professor Xing during the Fall '09 term at SUNY Stony Brook.

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