Description Usage Arguments Details Value Author(s) References Examples
View source: R/nlVarmethods.R
LogLikelihood method for VECM models.
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object 
object of class 
r 
The cointegrating rank. By default the rank specified in the call to

... 
additional arguments to 
The LogLikelihood 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_{t1}, …, Δ y_{tp}. 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 = \logΣ
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.
LogLikelihood value.
Matthieu Stigler
Hamilton (1994) Time Series Analysis, Princeton University Press
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