Model selection table

Find definitions and interpretation guidance for the Model Selection table.

The model selection table includes a row for every candidate model in the search that had estimable parameters. The table orders the model by decreasing fit so that the best model is in the first row.

In This Topic

Model
Log-likelihood
AIC, AICc and BIC

Model

The header of the model column provides the seasonal and nonseasonal orders of differencing for all the models in the table.

d: The order of nonseasonal differencing indicates the number of times you subtract the previous data value from the current data value.
D: The order of seasonal differencing indicates the number of times you subtract the previous season value from the current data value.

The rows show the order of the autoregressive and moving average terms for the models.

p: The order of the nonseasonal autoregressive term is the number of previous values (lags) that affect the current value.
q: The order of the nonseasonal moving average term is the number of previous error terms (lags of the forecast errors) that affect the current value.
P: The order of the seasonal autoregressive term is the number of lags from the previous season that are significantly correlated with the current season.

Q: The order of the seasonal moving average term is the number of previous error terms (lags of the forecast errors) from the previous season that affect the current value.

Log-likelihood

The analysis uses the log-likelihood for a model in the calculations for the information criteria.

Interpretation

Usually, you use the information criteria to compare models because the log-likelihood cannot decrease when you add terms to a model. For example, a model with 5 terms has higher log-likelihood than any of the 4-term models you can make with the same terms. Therefore, log-likelihood is most useful when you compare models of the same size. For models with the same number of terms, the higher the log-likelihood, the better the model fits the data.

AIC, AICc and BIC

The Akaike's Information Criterion (AIC), corrected Akaike’s Information Criterion (AICc), and the Bayesian Information Criterion (BIC) are measures of the relative quality of a model that account for fit and the number of terms in the model.

Interpretation

Use AIC, AICc and BIC to compare different models. Smaller values are desirable. However, the model with the least value for a set of terms does not necessarily fit the data well. Also use tests and plots to assess how well the model fits the data.

AICc and AIC: When the sample size is small relative to the parameters in the model, AICc performs better than AIC. AICc performs better because with relatively small sample sizes, AIC tends to be small for models with too many parameters. Usually, the two statistics give similar results when the sample size is large enough relative to the parameters in the model.
AICc and BIC: Both AICc and BIC assess the likelihood of the model and then apply a penalty for adding terms to the model. The penalty reduces the tendency to overfit the model to the sample data. This reduction can yield a model that performs better in general.; As a general guideline, when the number of parameters is small relative to the sample size, BIC has a larger penalty for the addition of each parameter than AICc. In these cases, the model that minimizes BIC tends to be smaller than the model that minimizes AICc.