# 420Hw13ans - STAT 420 Homework#13 Fall 2008 1 a > > > > > >...

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STAT 420 Fall 2008 Homework #13 1. a) > set.seed(1) #set seed for generating random sequecne > y0.5 <- arima.sim(n=100, model=list(ar=0.5)) #simulate AR(1) > par(mfrow=c(3,1)) #3 plots per page > ts.plot(y0.5) #plot series > acf(y0.5) #plot sample ACF > pacf(y0.5) #plot sample PACF PACF 1 0.5 = φ 1 , then PACF is “small” after lag 1. ACF “dies out”.

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b) > set.seed(1) > ym0.5 <- arima.sim(n=100, model=list(ar=-0.5)) > par(mfrow=c(3,1)) > ts.plot(ym0.5) > acf(ym0.5) > pacf(ym0.5) PACF 1 – 0.5 = φ 1 , then PACF is “small” after lag 1. ACF r k 1 k the first few lags as it “dies out”.
c) > set.seed(1) > may0.8 <- arima.sim(n=100, model=list(ma=0.8)) > par(mfrow=c(3,1)) > ts.plot(may0.8) > acf(may0.8) > pacf(may0.8) ACF is “small” after lag 1. PACF “dies out”.

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2. 10 58 40 57 35 71 48 59 41 55 64 + + + + + + + + + = y = 52.8. t y y y t - ( ) 2 y y t - ( ) ( ) 1 y y y y t t - - + ( ) ( ) 2 y y y y t t - - + 64 11.2 125.44 24.64 –132.16 55 2.2 4.84 –25.96
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## This note was uploaded on 05/09/2010 for the course MATH 420 taught by Professor Stepanov during the Spring '10 term at University of Illinois, Urbana Champaign.

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420Hw13ans - STAT 420 Homework#13 Fall 2008 1 a > > > > > >...

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