Selecting ARIMA orders based on ACF-PACF vs. auto.arima

Question

I use R to fit an ARIMA model to a time series (yearly granularity):

library(forecast)

beer <- c(150,241,361,403,504,684,706,862,879,806,840,846,1024,1196,1239,1237,1281,1342)

ts_beer = ts(beer, start = c(1980), frequency = 1)

dif.ts_beer <- diff(ts_beer)

acf(dif.ts_beer)
pacf(dif.ts_beer)

Based on the ACF and PACF, I fit an ARIMA(4,0,4) model.

dif.ts_beer.fit <- arima(dif.Gas, order = c(4,0,4))

dif.ts_beer.fit

It looks OK. But then I run auto.arima:

auto.arima(dif.ts_beer)

It gives:

Series: dif.ts_beer 
ARIMA(0,0,0) with non-zero mean 

Coefficients:
         mean
      70.1176
s.e.  17.0359

sigma^2 estimated as 5242:  log likelihood=-96.4
AIC=196.81   AICc=197.67   BIC=198.48

So the manual ARIMA(4,0,4) is not a good choice for this case? If so, what ARIMA(p,d,q) model should I use?

Answer 1

First, it is very hard to use (P)ACF plots to identify ARIMA(p,d,q) models if both p and q are nonzero. See Hyndman & Athanasopoulos:

If p and q are both positive, then the plots do not help in finding suitable values of p and q.

Second, your peaks at lag 4 only barely exceed the confidence bands.

I would always prefer auto.arima() over parsing (P)ACF plots myself, i.e., the Box-Jenkins approach. It is built by experts with a lot of experience, and it truly is a gold standard for ARIMA modeling, unless you are an expert yourself and you are working academically on the frontiers of knowledge.

In the present case, auto.arima() would prefer a simple mean model. I would recommend that you run with this.