gen_vec: Vector Error Correction Model Input

In franzmohr/bvartools: Bayesian Inference of Vector Autoregressive and Error Correction Models

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,
  r = NULL,
  const = NULL,
  trend = NULL,
  seasonal = NULL,
  structural = FALSE,
  tvp = FALSE,
  sv = FALSE,
  fcst = NULL,
  iterations = 50000,
  burnin = 5000
)

Arguments

data	a time-series object of endogenous variables.
p	an integer vector of the lag order of the series in the (levels) VAR. Thus, the resulting model's lag will be p - 1. See 'Details'.
exogen	an optional time-series object of external regressors.
s	an optional integer vector of the lag order of the exogenous variables of the series in the (levels) VAR. Thus, the resulting model's lag will be s - 1. See 'Details'.
r	an integer vector of the cointegration rank. See 'Details'.
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 will be automatically detected and depends on the frequency of the time-series object provided in data.
structural	logical indicating whether data should be prepared for the estimation of a structural VAR model.
tvp	logical indicating whether the model parameters are time varying.
sv	logical indicating whether time varying error variances should be estimated by employing a stochastic volatility algorithm.
fcst	integer. Number of observations saved for forecasting evaluation.
iterations	an integer of MCMC draws excluding burn-in draws (defaults to 50000).
burnin	an integer of MCMC draws used to initialize the sampler (defaults to 5000). These draws do not enter the computation of posterior moments, forecasts etc.

Details

The function produces the variable matrices of vector error correction (VEC) models, 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.

If an integer vector is provided as argument p, s or r, the function will produce a distinct model for all possible combinations of those specifications.

If tvp is TRUE, the respective coefficients of the above model are assumed to be time varying. If sv is TRUE, the error covariance matrix is assumed to be time varying.

Value

An object of class 'bvecmodel', which contains the following elements:

data	A list of data objects, which can be used for posterior simulation. Element Y is a time-series object of dependent variables. Element W is a timer-series object of variables in the cointegration term and element X is a time-series object of variables that do not enter the cointegration term. Element SUR contains a matrix of element X in its SUR form.
model	A list of model specifications.

References

Lütkepohl, H. (2006). New introduction to multiple time series analysis (2nd ed.). Berlin: Springer.

Examples

# Load data
data("e6")

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

franzmohr/bvartools documentation built on Jan. 28, 2024, 4:06 a.m.