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# hw4 - ARIMA(0 1 ×(1 0 12 model with Φ = 0 8 and θ = 0 5...

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The homework has to be stapled. PSTAT 174/274. Homework #4 Name: Due: 11/15/06 at the beginning of the class Score: /10 Credit: People you worked with: Sources consulted(Reference): 1. (2 points) Suppose y t = β 0 + β 1 t + · · · + β q t q + x t , β q = 0 , where x t is stationary. First, show that k x t is stationary for any k = 1 , 2 , · · · , and then show that k y t is not stationary for k < q , but is stationary for k q . 2. (1 points each) Consider the seasonal ARIMA model x t = w t + Θ w t - 2 . (a) Identify the model using the notation ARIMA ( P, D, Q ) s . (b) Show that the series is invertible | Θ | < 1 and find the coefficients in the representation w t = k =0 π k x t - k
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Unformatted text preview: ARIMA (0 , , 1) × (1 , , 0) 12 model with Φ = 0 . 8 and θ = 0 . 5. 4. (1 point each) Calculate and plot the impulse weights for the following transfer functions. (a) ν ( B ) = B/ (1 ± . 8 B ) (b) ν ( B ) = (3 + 2 B ) / (1 + 0 . 6 B ) 5. (2 points) Consider the following ARMA(1,1) process: (1 ± . 4 B ) x t = (1 + 0 . 8 B ) w t , where w t is a white noise series with zero mean and constatnt variance 1. Calculate the cross correlation function between x t and w t ....
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