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Unformatted text preview: 7. Find the moving average representation, the impulse response, and the forecast of each of the following processes: a) (1φ L)Y t = ε t , b) (1L)Y t = α + t , c) Y t = (1+ θ L) t , and d) Y t = α + (1+ L) t . 8. Consider the secondorder autoregressive process y t = a + a 2 y t2 + t ,where ⏐ a 2 ⏐ < 1. a. Find: i. E t2 y t ii. E t1 y t iii. E t y t +2 iv. Cov( y t , y t1 ) v. Cov( y t , y t2 ) vi. the partial autocorrelations 11 and 22 b. Find the impulse response function. Given y t2 , trace out the effects on an t shock on the { y t } sequence. c. Determine the forecast function: E t y t + s . The forecast error ) ( s e t is the difference between y t + s and E t y t + s . Derive the correlogram of the { ) ( s e t } sequence. [Hint: Find E t ) ( s e t , Var [ ] ) ( s e t , and [ ] ) ( ) ( j s e s e E t t t − for j = 0 to s ]. 9. Enders, chapter 2, question 11....
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This note was uploaded on 09/29/2010 for the course ECON Econometri taught by Professor Fairlie during the Winter '09 term at University of California, Santa Cruz.
 Winter '09
 Fairlie

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