aicbic (GARCH Toolbox)

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

Syntax

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

Arguments

LogLikelihood
Vector of optimized log-likelihood objective function (LLF) values associated with parameter estimates of the models to be tested. aicbic assumes 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 LogLikelihood. NumParams can be a scalar applied to all values in LogLikelihood, or a vector the same length as LogLikelihood. 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 LogLikelihood. NumObs can be a scalar applied to all values in LogLikelihood, or a vector the same length as LogLikelihood. It is required to compute BIC. All elements of NumObs must be positive integers.

`LogLikelihood`	Vector of optimized log-likelihood objective function (LLF) values associated with parameter estimates of the models to be tested. `aicbic` assumes 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 `LogLikelihood`. `NumParams` can be a scalar applied to all values in `LogLikelihood`, or a vector the same length as `LogLikelihood`. 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 `LogLikelihood`. `NumObs` can be a scalar applied to all values in `LogLikelihood`, or a vector the same length as `LogLikelihood`. It is required to compute BIC. All elements of `NumObs` must be positive integers.

Description

aicbic computes the Akaike and Bayesian information criteria, using optimized log-likelihood objective function (LLF) values as input. You can obtain the LLF values by fitting models of the conditional mean and variance to a univariate return series.

AIC = aicbic(LogLikelihood, NumParams) computes only the Akaike (AIC) information criteria.

[AIC, BIC] = aicbic(LogLikelihood, NumParams, NumObs) computes both the Akaike (AIC) and Bayesian (BIC) information criteria.

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

AIC
Vector of AIC statistics associated witin this "Arguments" sectionh each LogLikelihood objective function value. The AIC statistic is defined as:

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

`AIC`	Vector of AIC statistics associated witin this "Arguments" sectionh each `LogLikelihood` objective function value. The AIC statistic is defined as:
`BIC`	Vector of BIC statistics associated with each `LogLikelihood` objective function value. The BIC statistic is defined as:

See Also
garchdisp, garchfit, garchinfer

Reference

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

Functions - Alphabetical List archtest