Why ACF not plotting lags

Question

Hi does anyone know why my ACF is not plotting my lag max when for my time series? You can use the airpassenger data in R for this question.

My code is:

acf(z.t, lag.max = 40, main = expression(paste("acf of Z"[t])))

and I'm getting

but want have 1-40 on the x-axis.

Answer 1

The data is a time series by month. Forty lags spans a range of 40 months, or 3.33 years. The time unit on the x-axis is denominated in years and you're seeing lags of 0 to 40 months in the graph.

As another example, if you run acf(AirPassengers, lag.max=12) you can see that the x-axis has lags from 0 to 12 months and the axis is labeled from zero to 1 year.

You can relabel the axis if you wish. For example:

mx=40
acf(AirPassengers, lag.max=mx, xaxt="n", xlab="Lag (months)")
axis(1, at=0:mx/12, labels=0:mx)

Answer 2

That's because the units of the axis are in seasonal units (periods), not time units.

frequency(AirPassengers) gives 12, so monthly. The axis in your plot goes to ~3.33, which is precisely 40 / 12.

You can get the values to generate your own plot from acf with x = acf(AirPassengers, lag.max = 40) and getting x$acf and x$lag .

You can also do:

library(forecast)
Acf(AirPassengers, lag.max = 40)