STATS – How a Auto Regressive Series and Moving Average Series Look Like

ACF of AR(1) is phi^h

ACF of MV(1) is theta/(1+theta^2) only for h=1 and 0 when h>1

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par(mfrow=c(4,2))
a1 <- arima.sim(list(order=c(1,0,0), ar=0.9), n=100)
plot(a1, ylab=”x”, main=(expression(AR(1)~~~phi==+.9)))
acf(a1)
a2 <- arima.sim(list(order=c(1,0,0), ar=-0.9), n=100)
plot(a2, ylab=”x”, main=(expression(AR(1)~~~phi==-.9)))
acf(a2)
a3 <- arima.sim(list(order=c(0,0,1), ma=0.5), n=100)
plot(a3, ylab=”x”, main=(expression(MA(1)~~~theta==+.5)))
acf(a3)
a4 <- arima.sim(list(order=c(0,0,1), ma=-0.5), n=100)
plot(a4, ylab=”x”, main=(expression(MA(1)~~~phi==-.5)))
acf(a4)

 

ARMA

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