gen_vec {bvartools} | R Documentation |
gen_vec
produces the input for the estimation of a vector error correction (VEC) model.
gen_vec(data, p = 2, exogen = NULL, s = 2, const = NULL, trend = NULL, seasonal = NULL)
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 ( |
trend |
a character specifying whether a trend term enters the error correction
term ( |
seasonal |
a character specifying whether seasonal dummies should be included in the error
correction term ( |
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.
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. |
Lütkepohl, H. (2007). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.
data("e6") data <- gen_vec(e6, p = 4, const = "unrestricted", season = "unrestricted")