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th1-840-08

# th1-840-08 - 3 Consider the process y t = ε t ε 2 t-1...

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First take home exercise, Econ 840 De Jong, Spring 2008 Answer all questions below. Please hand in your solutions at the start of the class of Wednes- day April 9. 1. Consider the MA(3) process y t = ε t - (11 / 4) ε t - 1 + (13 / 8) ε t - 2 - (1 / 4) ε t - 3 . What will be the equivalent MA(3) process that has all its roots outside the unit circle? Note: 1 - (11 / 4)0 . 5 + (13 / 8)0 . 5 2 - (1 / 4)0 . 5 3 = 0. 2. Overdiferencing happens when we diFerenced a time series when we should not have done so. Suppose that y t = ε t , where ε t is white noise. What will the autocorrelation function of Δ y t look like?
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Unformatted text preview: 3. Consider the process y t = ε t + ε 2 t-1 , where ε t is i.i.d. and distributed as N (0 , 1). Calculate the autocorrelation function of y t . 4. Consider the lag polynomial a ( L ) = ∑ p j =0 a j L j , for which the a j are real-valued. As-sume that a ( z ) has all its roots outside the unit circle. (a) Why will a (1) /a (0) > 0 if all roots are real-valued? (b) (hard) Why will a (1) /a (0) > 0 always (i.e. also if some roots are possibly complex-valued)? 1...
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