# solution6 - Y t-2 + u t , Q 3 E14.1 a. The mean of...

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Suggested Solutions to PS 6 * Hongyan Zhao Dec 8, 2009 Q 2 14.1 (a) Since the probability distribution of Y t is the same as the probability distribution of Y t - 1 (this is the deﬁnition of stationarity), the means (and all other moments) are the same. (b) E ( Y t ) = β 0 + β 1 E ( Y t - 1 ) + E ( u t ), E ( u t ) = 0 and E ( Y t ) = E ( Y t - 1 ). Thus E ( Y t ) = β 0 + β 1 E ( Y t ), and solving for E ( Y t ), we get E ( Y t ) = β 0 1 - β 1 . 14.9 (a) E ( Y t ) = β 0 + E ( e t ) + b 1 E ( e t - 1 ) + · · · + b q E ( e t - q ) = β 0 , because E ( e t ) = 0 for all values of t. (b) var ( Y t ) = var ( e t ) + b 2 1 var ( e t - 1 ) + · · · + b 2 q var ( e t - q ) + 2 b 1 cov ( e t , e t - 1 ) + · · · + 2 b q - 1 b q cov ( e t - q +1 , e t - q ) = σ 2 e (1 + b 2 1 + · · · + b 2 q ) because var ( e t ) = σ 2 e for all t and cov ( e t , e i ) = 0 for i 6 = t . 14.11 Write the model as Y t - Y t - 1 = β 0 + β 1 ( Y t - 1 - Y t - 2 ) + u t . Rearranging it, and get Y t = β 0 + (1 + β 1 ) Y t - 1 - β 1

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Unformatted text preview: Y t-2 + u t , Q 3 E14.1 a. The mean of quarterly growth rate (Δ Y t = ln ( GDP t /GDP t-1 )) is 0.0083. b. The mean growth rate in percentage points at an annual rate (400 * Δ Y t ) is 3.32. c. The standard deviation of Δ Y t is 0.0092. Standard deviation in percentage points at an annual rate is 3.68. d. Estimated Autocorrelations (unit free) Lags Autocorrelation 1 0.29 2 0.17 3 0.03 4-0.02 * If you ﬁnd any mistake or typo, please email me [email protected] 1 E14.6 2...
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## This note was uploaded on 02/17/2010 for the course ECON 141 taught by Professor Staff during the Fall '08 term at University of California, Berkeley.

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solution6 - Y t-2 + u t , Q 3 E14.1 a. The mean of...

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