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Highlights
Model selection for ARIMA and ARFIMA models
AIC, BIC, and HQIC information criteria
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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.
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.
. webuse usmacro (Federal Reserve Economic Data - St. Louis Fed) . arimasoc ogap, maxar(4) maxma(3) Fitting models (20): .................... done Lag-order selection criteria Sample: 1954q3 thru 2010q4 Number of obs = 226
| Model | LL df AIC BIC HQIC | |
| ARMA(0,0) | -549.4036 2 1102.807 1109.648 1105.568 | |
| ARMA(0,1) | -435.0753 3 876.1507 886.4123 880.2919 | |
| ARMA(0,2) | -361.249 4 730.4981 744.1802 736.0196 | |
| ARMA(0,3) | -330.844 5 671.6879 688.7906 678.5898 | |
| ARMA(1,0) | -292.3313 3 590.6625 600.9241 594.8037 | |
| ARMA(1,1) | -281.5762 4 571.1524 584.8345 576.6739 | |
| ARMA(1,2) | -275.3697 5 560.7395 577.8422 567.6414 | |
| ARMA(1,3) | -274.029 6 560.058 580.5812 568.3403 | |
| ARMA(2,0) | -276.5956 4 561.1912 574.8733 566.7127 | |
| ARMA(2,1) | -273.9052 5 557.8104 574.9131 564.7123 | |
| ARMA(2,2) | -273.2799 6 558.5599 579.0831 566.8422 | |
| ARMA(2,3) | -273.2587 7 560.5174 584.4611 570.1801 | |
| ARMA(3,0) | -273.2421 5 556.4843 573.587 563.3862 | |
| ARMA(3,1) | -273.1883 6 558.3766 578.8998 566.6589 | |
| ARMA(3,2) | -273.0747 7 560.1494 584.0931 569.8121 | |
| ARMA(3,3) | -272.9944 8 561.9888 589.3531 573.0319 | |
| ARMA(4,0) | -273.2006 6 558.4012 578.9244 566.6835 | |
| ARMA(4,1) | -273.0027 7 560.0055 583.9492 569.6682 | |
| ARMA(4,2) | -273.071 8 562.142 589.5063 573.1851 | |
| ARMA(4,3) | -272.9868 9 563.9735 594.7584 576.397 | |
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)
Read more about ARIMA and ARFIMA model selection in the Stata Time-Series Reference Manual; see [TS] arimasoc and [TS] arfimasoc.
View all the new features in Stata 18 and, in particular, New in time series.
