Want to find the best ARIMA or ARFIMA model for your data? Compare potential models using AIC, BIC, and HQIC. Use the new arimasoc and arfimasoc commands to select the best number of autoregressive and moving-average terms.
Researchers using autoregressive moving-average (ARMA) models must decide on the proper number of lags to include for the autoregressive and moving-average parameters in their models. Information criteria, which balance model fit against model parsimony, often guide the choice of the maximum number of lags.
arimasoc and arfimasoc assist in model selection by fitting a collection of autoregressive integrated moving average (ARIMA) or autoregressive fractionally integrated moving average (ARFIMA) models and computing information criteria for each model. arimasoc and arfimasoc compute the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and the Hannan–Quinn information criterion (HQIC). The selected model is the one with the lowest value of the information criterion.
Let’s see it work
We would like to fit an ARMA model for the output gap. We use arimasoc to fit candidate models with a maximum autoregressive lag of 4 and a maximum moving average lag of 3.
The output table provides information about each model, including the maximized log likelihood, the number of parameters estimated, and the AIC, BIC, and HQIC.
Below the output table, the selected model from each criterion is listed. The log-likelihood is maximized for the model with the most parameters, the ARMA(4,3). The AIC, BIC, and HQIC all select the more parsimonious ARMA(3,0) model for the output gap. We can now fit our selected model
. arima ogap, arima(3,0,0) (output omitted)
and proceed to investigate model predictions, forecasts, etc.
Fitting an ARFIMA model instead of an ARIMA model? Instead of typing
. arimasoc y, maxvar(4) maxma(3)
you type
. arfimasoc y, maxvar(4) maxma(3)