gen_vec

0th

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Vector Error Correction Model Input

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: $$\Delta y_t = \Pi w_t + \sum_{i=1}^{p-1} \Gamma_i \Delta y_{t - i} + \sum_{i=0}^{s-1} \Upsilon_i \Delta x_{t - i} + C^{UR} d^{UR}_t + u_t,$$ where $\Delta y_t$ is a $K \times 1$ vector of differenced endogenous variables, $w_t$ is a $(K + M + N^{R}) \times 1$ vector of cointegration variables, $\Pi$ is a $K \times (K + M + N^{R})$ matrix of cointegration parameters, $\Gamma_i$ is a $K \times K$ coefficient matrix of endogenous variables, $\Delta x_t$ is a $M \times 1$ vector of differenced exogenous regressors, $\Upsilon_i$ 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 $$Y = \Pi W + \Gamma X + U,$$ 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

L<U+00FC>tkepohl, H. (2007). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.

• gen_vec
Examples
# NOT RUN {
data("e6")
data <- gen_vec(e6, p = 4, const = "unrestricted", season = "unrestricted")

# }

Documentation reproduced from package bvartools, version 0.0.1, License: GPL (>= 2)

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