# logLik.VECM: Extract Log-Likelihood In tsDyn: Nonlinear Time Series Models with Regime Switching

## Description

Log-Likelihood method for VECM models.

## Usage

 1 2 ## S3 method for class 'VECM' logLik(object, r, ...) 

## Arguments

 object object of class VECM computed by VECM. r The cointegrating rank. By default the rank specified in the call to VECM, but can be set differently by user. ... additional arguments to logLik.

## Details

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.

## Value

Log-Likelihood value.

Matthieu Stigler

## References

Hamilton (1994) Time Series Analysis, Princeton University Press

## Examples

 1 2 3 4 5 6 data(zeroyld) data<-zeroyld #Fit a VAR vecm<-VECM(data, lag=1,r=1, estim="ML") logLik(vecm) 

tsDyn documentation built on June 4, 2018, 1:04 a.m.