gen_vec {bvartools}R Documentation

Vector Error Correction Model Input

Description

gen_vec produces the input for the estimation of a vector error correction (VEC) model.

Usage

gen_vec(data, p = 2, exogen = NULL, s = 2, const = NULL,
  trend = NULL, seasonal = NULL)

Arguments

data

a time-series object of endogenous variables.

p

an integer of the lag order of the series (levels) in the VAR.

exogen

an optional time-series object of external regressors.

s

an optional integer of the lag order of the exogenous variables of the series (levels) in the VAR.

const

a character specifying whether a constant term enters the error correction term ("restricted") or the non-cointegration term as an "unrestricted" variable. If NULL (default) no constant term will be added.

trend

a character specifying whether a trend term enters the error correction term ("restricted") or the non-cointegration term as an "unrestricted" variable. If NULL (default) no constant term will be added.

seasonal

a character specifying whether seasonal dummies should be included in the error correction term ("restricted") or in the non-cointegreation term as "unrestricted" variables. If NULL (default) no seasonal terms will be added. The amount of dummy variables depends on the frequency of the time-series object provided in data.

Details

The function produces the variable matrices of a vector error correction (VEC) model, which can also include exogenous variables:

Δ y_t = Π w_t + ∑_{i=1}^{p-1} Γ_i Δ y_{t - i} + ∑_{i=0}^{s-1} Υ_i Δ x_{t - i} + C^{UR} d^{UR}_t + u_t,

where Δ y_t is a K \times 1 vector of differenced endogenous variables, w_t is a (K + M + N^{R}) \times 1 vector of cointegration variables, Π is a K \times (K + M + N^{R}) matrix of cointegration parameters, Γ_i is a K \times K coefficient matrix of endogenous variables, Δ x_t is a M \times 1 vector of differenced exogenous regressors, Υ_i is a K \times M coefficient matrix of exogenous regressors, d^{UR}_t is a N \times 1 vector of deterministic terms, and C^{UR} is a K \times N^{UR} coefficient matrix of deterministic terms that do not enter the cointegration term. p is the lag order of endogenous variables and s is the lag order of exogenous variables of the corresponding VAR model. u_t is a K \times 1 error term.

In matrix notation the above model can be re-written as

Y = Π W + Γ X + U,

where Y is a K \times T matrix of differenced endogenous variables, W is a (K + M + N^{R}) \times T matrix of variables in the cointegration term, X is a (K(p - 1) + Ms + N^{UR}) \times T matrix of differenced regressor variables and unrestricted deterministic terms. U is a K \times T matrix of errors.

Value

A list containing the following elements:

Y

a matrix of differenced dependent variables.

W

a matrix of variables in the cointegration term.

X

a matrix of non-cointegration regressors.

References

Lütkepohl, H. (2007). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.

Examples

data("e6")
data <- gen_vec(e6, p = 4, const = "unrestricted", season = "unrestricted")


[Package bvartools version 0.0.2 Index]