tsDyn (version 0.9-32)

logLik.nlVar: Extract Log-Likelihood

Description

Log-Likelihood method for VAR models.

Usage

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

Arguments

object

object of class VAR computed by lineVar.

...

additional arguments to logLik.

Value

• Log-Likelihood value.

Details

The Log-Likelihood is computed as in Luetkepohl (2006) equ. 3.4.5 (p. 89) and Juselius (2006) p. 56:

$$LL = -(TK/2) \log(2\pi) - (T/2) \log|\Sigma| - (1/2) \sum^{T} \left [ (y_t - A^{'}x_t)^{'} \Sigma^{-1} (y_t - A^{'}x_t) \right ]$$ Where $\Sigma$ is the Variance matrix of residuals, and $x_t$ is the matrix stacking the regressors (lags and deterministic).

However, we use a computationally simpler version:

$$LL = -(TK/2) \log(2\pi) - (T/2) \log|\Sigma| - (TK/2)$$

See Juselius (2006), p. 57.

(Note that Hamilton (1994) 11.1.10, p. 293 gives $+ (T/2) \log|\Sigma^{-1}|$, which is the same as $-(T/2) \log|\Sigma|)$.

References

Hamilton (1994) Time Series Analysis, Princeton University Press

Juselius (2006) The Cointegrated VAR model: methodology and Applications, Oxford Univesity Press

Luetkepohl (2006) New Introduction to Multiple Time Series Analysis, Springer

Examples

data(zeroyld)
data<-zeroyld

#Fit a VAR
VAR<-lineVar(data, lag=1)
logLik(VAR)