Extract Log-Likelihood
Log-Likelihood method for VECM models.
## S3 method for class 'VECM' logLik(object, r, ...)
The Log-Likelihood is computed in two dfferent ways, depending on whether the
VECM was estimated with ML (Johansen) or 2OLS (Engle and Granger).
When the model is estimated with ML, the LL is computed as in Hamilton (1994) 20.2.10 (p. 637):
LL = -(TK/2) \log(2π) - (TK/2) -(T/2) \log|\hatΣ_{UU}| - (T/2) ∑_{i=1}^{r} \log (1-\hatλ_{i})
Where Σ_{UU} is the variance matrix of residuals from the first auxiliary regression, i.e. regressing Δ y_t on a constant and lags, Δ y_{t-1}, …, Δ y_{t-p}. λ_{i} are the eigenvalues from the Σ_{VV}^{-1}Σ_{VU}Σ_{UU}^{-1}Σ_{UV}, see 20.2.9 in Hamilton (1994).
When the model is estimated with 2OLS, the LL is computed as:
LL = \log|Σ|
Where Σ is the variance matrix of residuals from the the VECM model. There is hence no correspondance between the LL from the VECM computed with 2OLS or ML.
Log-Likelihood value.
Matthieu Stigler
Hamilton (1994) Time Series Analysis, Princeton University Press
data(zeroyld) data<-zeroyld #Fit a VAR vecm<-VECM(data, lag=1,r=1, estim="ML") logLik(vecm)
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