# test3solns - University of Toronto at Mississauga STA457H5F...

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pg. 1 Name (Print): Signature: Student Number: Aids Allowed: Any calculator without text keyboard 1. (6 marks) This question is about the stochastic process: y t = t ( 1+  t-1 ) where t is white noise with  2 = 2 a. (1 mark) What is E(y t )? Soln 0 b. (2 marks) What is Var(y t )? Soln 2 +  4 = 6 c. (2 marks) What is Cov(y t , y t-s ) for s = ±1, ±2, ±3, ±4, …. .? Soln Cov(y t , y t-s ) = Cov(y t , y t+s ) = 0 for s = ±1, ±2, ±3, ±4, …. . University of Toronto at Mississauga STA457H5F - Fall 2009 Term Test #3

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pg. 2 d. (1 mark) Is this process weakly stationary? Explain your answer. Soln Yes it is. Mean, variance, and autocovariances are all free of t. 2. (13 marks) This question is about the stochastic process: y t = 0 + 1 + 2 + +  t-1 + t where t is white noise with  2 = 1 a. (1 mark) What is E(y t | y t-1 , y t-2 , … , y 0 )? Soln
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test3solns - University of Toronto at Mississauga STA457H5F...

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