hwk4 - IEOR E4709 Data Analysis for Financial Engineers...

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Unformatted text preview: IEOR E4709 Data Analysis for Financial Engineers Solution 4 Problem 2.2 in Tsays : Solution Taking expectation of the model, we have E ( ) = 0 01 + 0 2 E ( 2 ) Therefore, E ( ) = 01 1 2 = 0 0125 . Taking variance of the model, we obtain Var ( ) = 0 04 Var ( 2 ) + 2 Therefore, Var ( ) = 02 1 04 = 0 0208 . For autocorrelation function, we may drop the constant term and multiply the equation by to obtain = 0 2 2 + Taking the expectation for , we have = 0 2 2 , where is the lag- autocoveriance of . Therefore, = 0 2 2 for . We know that = 1 . For = 1 , we use = to obtain 1 = 0 2 1 = 0 2 . This implies 1 = 0 . Therefore, = 2 2 for even number ; for odd number . For 1-step ahead forecast at = 100 , we have 101 = 0 01+0 2 99 + 101 . Taking conditional expectation, 100 (1) = 0 01 + 0 2 00 = 0 014 The forecast error is 100 (1) = 101 with mean and standard deviation = 02 = 141 . For 2-step ahead forecast, use...
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hwk4 - IEOR E4709 Data Analysis for Financial Engineers...

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