I'm currently doing some univariate forecasting using a small data set of about 36 observations and R software for analysis.
I've found that the basic visual inspection of ACFs and PACFs coupled with ADF tests for checking for stationarity yields different lag selection than it does when using information criterion.
for example when using visual inspection of the data it would appear that the appropriate lag selection for this model would be an AR(1),
However upon running the command
auto.arima() I find that the results are very different from my visual inspection.
Series: sample ARIMA(2,0,2) with non-zero mean Coefficients: ar1 ar2 ma1 ma2 mean 1.8850 -0.9482 -1.5561 0.7891 725.9292 s.e. 0.0471 0.0443 0.2045 0.2472 19.7146 sigma^2 estimated as 1136: log likelihood=-177.03
In terms of model selection which method of selection is preferred? Visual inspection of ACF and PACF or the use of a selected Information criterion?