BIC.varlse {bvhar}

Bayesian Information Criterion of Multivariate Time Series Model

Description

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

Usage

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

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

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

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

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

Arguments

object

Model fit

...

not used

Details

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{s - k}{n} \hat{\Sigma}_e

Then

BIC(p) = \log \det \Sigma_e + \frac{\log s}{s}(\text{number of freely estimated parameters})

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

Value

BIC value.

References

Gideon Schwarz. (1978). Estimating the Dimension of a Model. Ann. Statist. 6 (2) 461 - 464.

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