Final exam (2008Winter)

# Final exam (2008Winter) - University of Toronto STA457H1...

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University of Toronto STA457H1 S/STA2202H S Time Series Analysis Final Exam (April 29, 2008) Exam time: 0700-1000 pm Name Student number Course number 1

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Question 1) Define and Explain a. (10%) I(0) , I(1) and I(d) processes (processes of integrated of order zero, one and d ) b. (10%) Spurious regression and I(1) processes c. (10%) Cointegration d. (10%) Generalized autoregressive conditional heteroscedasticity (GARCH) model Question 2) Vector autoregressive (VAR) models and Granger causality test a. (5%) Consider a bivariate VAR(1) model + = - - t t t t t t a a X X X X , 2 , 1 1 , 2 1 , 1 , 2 , 1 5 . 0 4 . 0 1 . 0 5 . 0 , where ) , ( ~ ) , ( 2 , 2 , 1 Σ 0 N a a T t t , N 2 is a bivariate normal distribution with mean vector T ) 0 , 0 ( and covariance matrix = Σ 2 5 . 0 5 . 0 1 . Is this VAR(1) model stationary? b.
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Final exam (2008Winter) - University of Toronto STA457H1...

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