| AIC.varlse {bvhar} | R Documentation |
Akaike's Information Criterion of Multivariate Time Series Model
Description
Compute AIC of VAR(p), VHAR, BVAR(p), and BVHAR
Usage
## S3 method for class 'varlse'
AIC(object, ...)
## S3 method for class 'vharlse'
AIC(object, ...)
## S3 method for class 'bvarmn'
AIC(object, ...)
## S3 method for class 'bvarflat'
AIC(object, ...)
## S3 method for class 'bvharmn'
AIC(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}{s} \hat{\Sigma}_e
Then
AIC(p) = \log \det \Sigma_e + \frac{2}{s}(\text{number of freely estimated parameters})
where the number of freely estimated parameters is mk, i.e. pm^2 or pm^2 + m.
Value
AIC value.
References
Akaike, H. (1969). Fitting autoregressive models for prediction. Ann Inst Stat Math 21, 243–247.
Akaike, H. (1971). Autoregressive model fitting for control. Ann Inst Stat Math 23, 163–180.
Akaike H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, vol. 19, no. 6, pp. 716-723.
Akaike H. (1998). Information Theory and an Extension of the Maximum Likelihood Principle. In: Parzen E., Tanabe K., Kitagawa G. (eds) Selected Papers of Hirotugu Akaike. Springer Series in Statistics (Perspectives in Statistics). Springer, New York, NY.
Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis. Springer Publishing.