BIC evaluates model fit while penalizing the number of parameters. Its penalty is the parameter count multiplied by the natural logarithm of the sample size, so the penalty strengthens as datasets grow. Lower BIC values indicate a preferable balance of fit and simplicity. section 7.3.10
Use BIC when comparing competing models fitted to the same data:
- Prefer the model with the lower BIC when avoiding overfitting and favoring parsimony are priorities. section 7.3.10
- Interpret BIC alongside log likelihood and related criteria such as AIC and HQIC rather than treating fit alone as sufficient. section 7.3.10
- Compare BIC values for models trained on the same observations, including alternative time-series specifications. section 7.3.10 section 7.4.7
Comparing Holt–Winters and ARIMA
A fitted Holt–Winters model reports BIC = 223.54401397788672. Its BIC is lower than the corresponding ARIMA model's value, supporting Holt–Winters as the better-fitting, more parsimonious choice in this comparison. The result is also consistent with its slightly more accurate forecast. section 7.4.7
>>> print(f"AIC: {hw_model.aic}")
AIC: 198.23435477953498
>>> print(f"BIC: {hw_model.bic}")
BIC: 223.54401397788672
Inspect the fitted Holt–Winters model's AIC and BIC values directly. section 7.4.7
