HQ: Hannan-Quinn Criterion

In bvhar: Bayesian Vector Heterogeneous Autoregressive Modeling

Hannan-Quinn Criterion

Description

Compute HQ of VAR(p), VHAR, BVAR(p), and BVHAR

Usage

HQ(object, ...)

## S3 method for class 'logLik'
HQ(object, ...)

## S3 method for class 'varlse'
HQ(object, ...)

## S3 method for class 'vharlse'
HQ(object, ...)

## S3 method for class 'bvarmn'
HQ(object, ...)

## S3 method for class 'bvarflat'
HQ(object, ...)

## S3 method for class 'bvharmn'
HQ(object, ...)

Arguments

object	A logLik object or Model fit
...	not used

Details

The formula is

HQ = -2 \log p(y \mid \hat\theta) + k \log\log(T)

which can be computed by AIC(object, ..., k = 2 * log(log(nobs(object)))) with stats::AIC().

Let \tilde{\Sigma}_e be the MLE and let \hat{\Sigma}_e be the unbiased estimator (covmat) for \Sigma_e. Note that

\tilde{\Sigma}_e = \frac{n - k}{T} \hat{\Sigma}_e

Then

HQ(p) = \log \det \Sigma_e + \frac{2 \log \log n}{n}(\text{number of freely estimated parameters})

where the number of freely estimated parameters is pm^2.

Value

HQ value.

References

Hannan, E.J. and Quinn, B.G. (1979). The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society: Series B (Methodological), 41: 190-195.

Hannan, E.J. and Quinn, B.G. (1979). The Determination of the Order of an Autoregression. Journal of the Royal Statistical Society: Series B (Methodological), 41: 190-195.

Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis. Springer Publishing.

Quinn, B.G. (1980). Order Determination for a Multivariate Autoregression. Journal of the Royal Statistical Society: Series B (Methodological), 42: 182-185.

bvhar documentation built on April 4, 2025, 5:22 a.m.