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, ...)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 \(pm^2\).
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.