5. Consider the p'th order autoregressive, AR(p). model X. = +x+6X, 2+...+0,X.,+€, where we assume that &, - iid WN(0,0%

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5 Consider The P Th Order Autoregressive Ar P Model X X 6x 2 0 X Where We Assume That Iid Wn 0 0 1 (28.72 KiB) Viewed 29 times

5. Consider the p'th order autoregressive, AR(p). model X. = +x+6X, 2+...+0,X.,+€, where we assume that &, - iid WN(0,0%); a. Define the characteristic polynomial for the AR(p) model. b. What is the stationarity and causality conditions for the AR(p) model? c. Derive the Yule Walker equations and express them in matrix form. d. For which parameter values for 6.0,,, does the AR(p) model have a unit root? e. What is the forecast fr. and #2 for fra and #2 respectively. Where 4,0......., are the estimates of the coefficients. f. Is the AR(3) model with = 0.4.0,=0.4, and 6) = 0.2 a unit root process? g. Is the AR(3) model with =-0.4.6),=-0.4, and 4 =-0.2 a unit root process?