# Estimation of Vector error correction model (VECM)

### Description

Estimate either a VECM by Engle-Granger or Johansen (MLE) method.

### Usage

 1 2 3 VECM(data, lag, r = 1, include = c("const", "trend", "none", "both"), beta = NULL, estim = c("2OLS", "ML"), LRinclude = c("none", "const", "trend", "both"), exogen = NULL) 

### Arguments

 data multivariate time series (first row being first=oldest value) lag Number of lags (in the VECM representation, see Details) r Number of cointegrating relationships include Type of deterministic regressors to include beta for VECM only: imposed cointegrating value. If null, will be estimated so values will be estimated estim Type of estimator: 2OLS for the two-step approach or ML for Johansen MLE LRinclude Type of deterministic regressors to include in the long-term relationship. Can also be a matrix with exogeneous regressors (2OLS only). exogen Inclusion of exogenous variables (first row being first=oldest value). Is either of same size than data (then automatically cut) or than end-sample.

### Details

This function is just a wrapper for the lineVar, with model="VECM".

More comprehensive functions for VECM are in package vars. A few differences appear in the VECM estimation:

Engle-Granger estimator

The Engle-Granger estimator is available

Presentation

Results are printed in a different ways, using a matrix form

lateX export

The matrix of coefficients can be exported to latex, with or without standard-values and significance stars

Prediction

The predict method contains a newdata argument allowing to compute rolling forecasts.

Two estimators are available: the Engle-Granger two step approach (2OLS) or the Johansen (ML). For the 2OLS, deterministics regressors (or external variables if LRinclude is of class numeric) can be added for the estimation of the cointegrating value and for the ECT. This is only working when the beta value is not pre-specified.

The arg beta is the cointegrating value, the cointegrating vector will be taken as: (1, -beta).

Note that the lag specification corresponds to the lags in the VECM representation, not in the VAR (as is done in package vars or software GRETL). Basically, a VAR with 2 lags corresponds here to a VECM with 1 lag. Lag 0 in the VECM is not allowed.

#'The arg beta allows to specify constrained cointegrating values, leading to ECT= β^{'}X_{t-1}. It should be specified as a K \times r matrix. In case of r=1, can also be specified as a vector. Note that the vector should be normalised, with the first value to 1, and the next values showing the opposite sign in the long-run relationship - β. In case the vector has K-1 values, this is what lineVar is doing, setting (1, - β). Note finally one should provide values for all the coefficients (eventually except for special case of r=1 and k-1), if you want to provide only part of the parameters, and let the others be estimated, look at the functions in package urca.

### Value

An object of class VECM (and higher classes VAR and nlVar) with methods:

Usual methods

Print, summary, plot, residuals, fitted, vcov

Fit criteria

AIC, BIC, MAPE, mse, logLik (latter only for models estimated with MLE)

Prediction

Predict and predict_rolling

VAR/VECM methods

Impulse response function (irf) and forecast error variance decomposition (fevd)

LaTeX

toLatex

### Author(s)

Matthieu Stigler

lineVar TVAR and TVECM for the correspoding threshold models. linear for the univariate AR model.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 data(zeroyld) data<-zeroyld #Fit a VECM with Engle-Granger 2OLS estimator: vecm.eg<-VECM(zeroyld, lag=2) #Fit a VECM with Johansen MLE estimator: vecm.jo<-VECM(zeroyld, lag=2, estim="ML") #compare results with package vars: if(require(vars)) { data(finland) #check long coint values all.equal(VECM(finland, lag=2, estim="ML", r=2)$model.specific$beta, cajorls(ca.jo(finland, K=3, spec="transitory"), r=2) $beta, check.attributes=FALSE) # check OLS parameters all.equal(t(coefficients(VECM(finland, lag=2, estim="ML", r=2))), coefficients(cajorls(ca.jo(finland, K=3, spec="transitory"), r=2)$rlm), check.attributes=FALSE) } ##export to Latex toLatex(vecm.eg) toLatex(summary(vecm.eg)) options("show.signif.stars"=FALSE) toLatex(summary(vecm.eg), parenthese="Pvalue") options("show.signif.stars"=TRUE)