CT6 Sep 13' Q9iv

[Edward Smith]

Hello,

In an MA(q) process where q>=1, the PACF tends to 0 but never completely cuts off...

Likewise, for an AR(p) process where p>=1, would we expect the ACF to tend to 0 but never completely cut off?

Also, for an ARMA(p,q), would we then expect neither the ACF or PACF to equal 0 when both p and q >=1?

Cheers

 

[Dave Johnson]

Hi Edward

Yes, that's correct. I've produced a plot to demonstrate this in R using the following code.

par(mfrow = c(3, 2))
barplot(ARMAacf(ar=.5, ma=c(), lag.max = 10), main = "AR(1) ACF")
barplot(ARMAacf(ar=.5, ma=c(), lag.max = 10, pacf = T), main = "AR(1) PACF", names.arg = 1:10)
barplot(ARMAacf(ar=c(), ma=.5, lag.max = 10), main = "MA(1) ACF")
barplot(ARMAacf(ar=c(), ma=.5, lag.max = 10, pacf = T), main = "MA(1) PACF", names.arg = 1:10)
barplot(ARMAacf(ar=.5, ma=.5, lag.max = 10), main = "ARMA(1,1) ACF")
barplot(ARMAacf(ar=.5, ma=.5, lag.max = 10, pacf = T), main = "ARMA(1,1) PACF", names.arg = 1:10)