11_29 - STAT 420 Examples for 11/29/2007 Fall 2007 1....

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Unformatted text preview: STAT 420 Examples for 11/29/2007 Fall 2007 1. Calculate r 1 and r 2 for the time series 16 22 19 25 18 ( Note: In practice reliable autocorrelation estimates are only obtained from series consisting of approximately 50 observations or more. ) r k = ( ) ( ) ( ) & & =- = +--- N N t t k t k t t y y y y y y 1 2 1 PACF Corr ( Y t , Y t + k | Y t + 1 , , Y t + k 1 ) Consider a regression type model Y t + k = k 1 Y t + k 1 + k 2 Y t + k 2 + + k k Y t + e t + k Consider Cov ( , Y t + k j ), j = 1, 2, , k . Divide by : & 1 = k 1 + k 2 1 + + k k k 1 2 = k 1 1 + k 2 + + k k k 2 k = k 1 k 1 + k 2 k 2 + + k k PACF ( k ) = Corr ( Y t , Y t + k | Y t + 1 , , Y t + k 1 ) = k k . k = 1 : 1 = 1 1 = 1 1 1 1 = 1 k = 2 : 1 = k 1 + k 2 1 2 = k 1 1 + k 2 2 1 = 2 1 2 1 1 1 -- 2 2 = 2 1 2 1 2 1 -- and so on AR(1) MA(1) k = k 1 = 2 1 +- k = 0, k > 1...
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11_29 - STAT 420 Examples for 11/29/2007 Fall 2007 1....

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