I'm using auto.arima
to get the best model for the MASS
dataset deaths
. However, auto.arima
does not seem to give the best model by measures of AIC, AICc, or BIC. auto.arima
code below:
> data(deaths, package='MASS')
> deaths
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
1974 3035 2552 2704 2554 2014 1655 1721 1524 1596 2074 2199 2512
1975 2933 2889 2938 2497 1870 1726 1607 1545 1396 1787 2076 2837
1976 2787 3891 3179 2011 1636 1580 1489 1300 1356 1653 2013 2823
1977 3102 2294 2385 2444 1748 1554 1498 1361 1346 1564 1640 2293
1978 2815 3137 2679 1969 1870 1633 1529 1366 1357 1570 1535 2491
1979 3084 2605 2573 2143 1693 1504 1461 1354 1333 1492 1781 1915
> library(forecast)
> auto.arima(deaths)
Series: deaths
ARIMA(1,0,0)(2,0,0)[12] with non-zero mean
Coefficients:
ar1 sar1 sar2 intercept
0.4418 0.3098 0.5078 2058.2234
s.e. 0.1345 0.0973 0.0998 175.8665
sigma^2 estimated as 79455: log likelihood=-515.07
AIC=1040.13 AICc=1041.04 BIC=1051.51
If I instead fit a ARIMA(2,1,1)x(1,1,1) model, it is better by all measures:
> Arima(deaths, order=c(2,1,1), seasonal=c(1,1,1))
Series: deaths
ARIMA(2,1,1)(1,1,1)[12]
Coefficients:
ar1 ar2 ma1 sar1 sma1
0.2729 -0.3270 -1.0000 -0.2985 -0.9999
s.e. 0.1356 0.1396 0.1305 0.1426 1.0106
sigma^2 estimated as 39753: log likelihood=-413.08
AIC=838.17 AICc=839.79 BIC=850.64