40057 - ) (a) Is the model stationary? (b) Identify the...

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STATISTICS 4005 ASSIGNMENT 7 1. Based on quarterly data, a seasonal model of the form Z t = Z t - 4 + a t - θ 1 a t - 1 - θ 2 a t - 2 has been fit to a certain time series. (a) Find the first four ψ -weights for this model. (b) Suppose that θ 1 = 0 . 5 , θ 2 = - 0 . 25, and σ a = 1 and that the data for the last four quarters are I II III IV Series 25 20 25 40 Residual 2 1 2 3 Find the forecasts for the next four quarters. (c) Find 95% prediction intervals for the forecasts in b. 2. An AR model has AR characteristic polynomial (1 - 1 . 6 x + 0 . 7 x 2 )(1 - 0 . 8 x 12
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Unformatted text preview: ) (a) Is the model stationary? (b) Identify the model as a certain seasonal ARIMA model. 3. For the seasonal model Z t = Φ Z t-4 + a t-θa t-1 with | Φ | < 1, find γ k and ρ k for k > 0. 4. Identify the following as certain multiplicative seasonal ARIMA models: (a) Z t = 0 . 5 Z t-1 + Z t-4-. 5 Z t-5 + a t-. 3 a t-1 (b) Z t = Z t-1 + Z t-12-Z t-13 + a t-. 5 a t-1-. 5 a t-12 + 0 . 25 a t-13...
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