GARCH Toolbox™Functions — Alphabetical List   archtest
  

aicbic

Calculate Akaike (AIC) and Bayesian (BIC) information criteria for model order selection

Syntax

AIC = aicbic(LLF,NumParams)
[AIC,BIC] = aicbic(LLF,NumParams,NumObs)

Description

Since information criteria penalize models with additional parameters, parsimony is the basis of the AIC and BIC model order selection criteria.

Input Arguments

LLF

Vector of optimized log-likelihood objective function (LLF) values associated with parameter estimates of the models to be tested. aicbic assumes that you obtained the LLF values from the estimation function garchfit or the inference function garchinfer.

NumParams

Number of estimated parameters associated with each LLF value in LLF. NumParams can be a scalar applied to all values in LLF, or a vector the same length as LLF. All elements of NumParams must be positive integers. Use garchcount to compute NumParams values.

NumObs

Sample size of the observed return series you associate with each value of LLF. NumObs can be a scalar applied to all values in LLF, or a vector the same length as LLF. It is required to compute BIC. All elements of NumObs must be positive integers.

Output Arguments

AIC

Vector of AIC statistics associated with each LLF objective function value. The AIC statistic is defined as

AIC = (-2*LLF) + (2*NumParams)

BIC

Vector of BIC statistics associated with each LLF objective function value. The BIC statistic is defined as

BIC = = (-2*LLF) + (NumParams * log(NumObs))

Examples

See Akaike and Bayesian Information Criteria.

See Also

garchdisp, garchfit, garchinfer

References

Box, G.E.P., G.M. Jenkins, and G.C. Reinsel, Time Series Analysis: Forecasting and Control, Third edition, Prentice Hall, 1994.

  

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