When first being exposed to methods of model selection in ARIMA class models, I was told that visual inspection of the ACF and PACF (when data is stationary) is satisfactory.
However when compared to the model selection using AIC or BIC we will end up with a different model sometimes.
Attached is the plot of time series data I'm using I am using along with its ACFs and PACFs. Visual inspection would lead us to conclude that the appropriate model would be an AR(1).
However based on the model from AIC (given by the R command auto.arima) the appropriate model is an ARMA(2,2).
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?
Visual inspection of the ACF and PACF can be quite inconclusive and misleading. This can be seen by simulating ARMA models and observing the unexpected inconclusive appearances of their ACFs and PACFs. The correlograms do not usually look as expected. It is usually a matter of trial and error to choose a model from a range of suggestive models. Automatic model selection criteria like the AIC and BIC provide better approach to model selection as the choice is based on their minimization.
For example the first 4 values of your ACF and the first PAC are significant giving suggestion of an ARMA(1,4); you chose an AR(1). The ARIMA(2,2) chosen by AIC is likely to be the most adequate of all contending models. However it is advised that many more selection criteria including R squared and out-of-sample forecast goodness-of-fit be used also.
Dear Jacob
The time series you are studying is not stationary. You should determine p and q after differencing your time series.
I think auto.arima is a very useful tool but is not enough. You should use a combination of both methods. To decide on a better method, you can compare the MSE values or study significance of the model coefficients.
Here are some observations
1-We investigate the ACF and PACF of the times series itself to see which model they suggest.
2-We check the ACF and PACF of the residual, after fitting a model to the time series, to see if this residual is a white noise.
3-We use an information criterion like AIC or BIC to choose among correctly fitted models.
4- From my own experience, depending on how complex your time series is, auto.arima() might not be the best modeling tool. Rather, you should use arima() and set its parameters based on the investigation you’ve already done on the AFC and PACF of your time series .
Hi,
Whatever the method you use to specify the order of the ARMA model, you need to evaluate the residuals of the fitted model, to finally decide the appropriate model for the underlying data. Indeed, it is iterative process and you can use both for the model identification.