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12_04_2 - Example 1 > > > > > > > > set.seed(1 y1 <...

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Example 1 : > set.seed(1) > y1 <- arima.sim(n=100, model=list(ma=-0.8)) > > par(mfrow=c(3,1)) > > ts.plot(y1) > acf(y1) > pacf(y1) ACF ( 0 ) = 1, ACF ( 1 ) is “big”, ACF is “small” after lag 1. PACF exponentially “dies out”. This behavior is consistent with MA ( 1 ) = ARMA ( 0, 1 ) .
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Example 2 : > set.seed(1) > y2 <- arima.sim(n=100, model=list(ar=c(0.5,0.3))) > > ts.plot(y2) > acf(y2) > pacf(y2) PACF ( 1 ) and PACF ( 2 ) are “big”, PACF is “small” after lag 2. ACF exponentially “dies out” after lag 2. This behavior is consistent with AR ( 2 ) = ARMA ( 2, 0 ) .
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Example 3 : > set.seed(1) > y3 <- arima.sim(n=100, model=list(ma=c(0.4,-0.3))) > > ts.plot(y3) > acf(y3) > pacf(y3) ACF ( 0 ) = 1, ACF ( 1 ) and ACF ( 2 ) “big” (barely), ACF is “small” after lag 2. PACF exponentially “dies out”. This behavior is consistent with MA ( 2 ) = ARMA ( 0, 2 ) .
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Example 4 : > set.seed(1) > y4 <- arima.sim(n=100, model=list(ar=c(0.7,-0.4),ma=0.6)) > > ts.plot(y4) > acf(y4) > pacf(y4) If we did not know that this is an ARMA ( 2, 1 ) time series and had to guess the appropriate model from the behavior of ACF and PACF, several different possible models could reasonably match the behavior of ACF and PACF. ARMA ( 2, 1 ) and ARMA ( 2, 4 ) are two reasonable guesses.
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