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HQIC

As explained in Statistics Every Programmer Needs

HQIC is an information criterion that balances model fit and parameter complexity using a sample-size-dependent penalty between those of AIC and BIC in growth rate.

HQIC evaluates competing time-series models by balancing goodness of fit against parameter complexity. Its sample-size-dependent penalty is stronger than AIC’s and weaker than BIC’s in growth rate, helping compare fit while discouraging unnecessary parameters. section 7.3.10

Interpret HQIC alongside the other model-fit measures:

  • Log likelihood measures how closely model parameters explain the observed data but does not account for model complexity. section 7.3.10
  • AIC penalizes added parameters and may favor more complex models in large data sets. section 7.3.10
  • BIC applies a stronger sample-size-dependent penalty and prioritizes simpler models when avoiding overfitting matters. section 7.3.10
  • HQIC uses twice the natural logarithm of the natural logarithm of sample size to scale its parameter penalty. section 7.3.10

How Statistics Every Programmer Needs covers it

How deep it goes
Defines HQIC and its penalty relative to AIC and BIC but does not provide a worked numerical calculation or implementation.
Examples
Uses goodness-of-fit reporting for fitted time-series models and contrasts HQIC with AIC and BIC.
What it assumes
Assumes familiarity with fitted time-series models, log likelihood, parameter counts, and sample size.
What you can do after
Evaluate competing fitted time-series models using fit and complexity criteria.
How it connects
Connects HQIC to log likelihood, AIC, BIC, model complexity, sample size, and overfitting.
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