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test4solns

# test4solns - model a(1-0.5L 2 y t = t b(1-0.5L(1 0.5L-0.2L...

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1 1. (7 marks) Refer to your R output for the time series of US dishwasher sales. a. (2 marks) Do you think the best model is probably (i) AR(p) or (ii) MA(q) or (iii) noise or (iv) something else? If you think it is AR(p), what do you suggest for p? If you think it is MA(q), what do you suggest for q? b. (5 marks) Hand in the PACF plot. Soln a) AR(1) b) – 2. ( 6 marks ) For a particular AR(3) process, the autocorrelations are (1) = 0.6, (2) =0, and (3) = -0.1. Use the Yule-Walker equations to evaluate the lag 1 and lag 2 partial autocorrelations, (1) and (2). Type equation here. Soln (1) = 1 = (1) = 0.6 To find (2).solve ( ߩ (1) ߩ (2) ) = 1 ߩ (1) ߩ (1) 1 ( ߙ 1 ߮ (2) ) giving (2) = ( (2) - (1) 2 )/ ( - (1) 2 )/ = -0.5625 3. (6 marks) Classify each of these ARIMA models. That is, state p, d, and q for each

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Unformatted text preview: model. a. (1-0.5L) 2 y t = t b. (1-0.5L) (1+0.5L-0.2L 2 ) (1+0.3L 2 ) 2 yt =(1-0.5L) (1-0.5L+0.2L 2 ) t Soln a) p=1, d=2, 1=0 b) p=4, d=2, q=2 University of Toronto at Mississauga STA457H5F - Fall 2009 Term Test #4 2 4. (4 marks) Classify this SARIMA model. That is, state p, d, q, P, D, Q, and s. -(1-0.5L-0.1L 4 )(1-0.5L 12 )(1-L 6 ) 2 (1-L) y t =(1+0.2L 6 ) t Soln S=6, P = 2, D=2, Q=1, p=4, d=1, q=0 5. (6 marks) For each set of ACF and PACF plots, suggest a model, AR(p), MA(q), or noise If you think it is AR(p), what do you suggest for p? If you think it is MA(q), what do you suggest for q? a. b. 3 Soln a) AR(4) b) MA(1) c) Noise...
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