sim_vecm_ardl: Generate data from a VECM/ARDL equation

In bootCT: Bootstrapping the ARDL Tests for Cointegration

Generate data from a VECM/ARDL equation

Description

Generate data from a VECM/ARDL equation

Usage

sim_vecm_ardl(
  nobs,
  case = 1,
  sigma.in = diag(3),
  gamma.in,
  Axx.in,
  ayxUC.in,
  ayy.in,
  mu.in,
  eta.in,
  azeroy.in = 0,
  aoney.in = 0,
  burn.in,
  seed.in = NULL
)

Arguments

nobs	number of observations.
case	case related to intercept and trend
sigma.in	error covariance matrix.
gamma.in	list of short-run parameter matrices
Axx.in	long-run relationships between the independent variables
ayxUC.in	long-run unconditional relationship between dependent and independent variables, \mathbf a_{yx}^{(UC)} . The second component ayxC, derived from conditioning, is calculated as\mathbf a_{yx}^{(C)}= - \boldsymbolω'\mathbf A_{xx}
ayy.in	long-run relationship for the dependent variable a_{yy}
mu.in	VAR intercept vector
eta.in	VAR trend vector
azeroy.in	Conditional ARDL intercept. Overridden if CASE I or CASE II
aoney.in	Conditional ARDL trend. Overridden if CASE IV
burn.in	burn-in number of observations
seed.in	optional seed number for random error generation.

Value

A list that includes

• dims: a vector with the dataset dimension

• case: the case given as input

• data: the generated data

• diffdata: the data first difference

• ut: the generated random error matrix.

• sigma: the error covariance matrix \boldsymbolΣ.

• omega: the \boldsymbolω vector of parameters generated via conditioning

• At: the conditional long-run parameter matrix \tilde{\mathbf A}

• ayx1: the unconditional subvector of the ARDL equation \mathbf a_{y.x}^{UC}

• ayx: the conditional subvector of the ARDL equation a_{y.x}=a_{y.x}^{UC}-ω'A_{xx}

• gammalist: the list of unconditional \boldsymbolΓ_j parameter matrices

• psilist: the list of conditional \boldsymbolψ_{y.x,j} parameter matrices

• azero: the unconditional VECM intercept

• azero.c: the conditional VECM intercept

• interc.ardl: the conditional ARDL intercept

• aone: the unconditional VECM trend

• aone.c: the conditional VECM trend

• interc.ardl: the conditional ARDL trend

• vmu: the VAR intercept

• veta: the VAR trend

Examples

#PARAMETERS

#Sigma
corrm = matrix(0, ncol = 3, nrow = 3)
corrm[2,1] = 0.25
corrm[3,1] = 0.4
corrm[3,2] = -0.25
Corrm = (corrm + t(corrm)) + diag(3)
sds = diag(c(1.3, 1.2, 1))
Sigma = (sds %*% Corrm %*% t(sds))

#Gamma
gammax=list()
gammax[[1]] = matrix(c(0.6, 0, 0.2, 0.1, -0.3, 0, 0, -0.3, 0.2), nrow = 3, ncol = 3, byrow = TRUE)
gammax[[2]] = matrix(c(0.2, 0, 0.1, 0.05, -0.15, 0, 0, 0, 0.1), nrow = 3, ncol = 3, byrow = TRUE)

#DATA GENERATION
data_sim = sim_vecm_ardl(nobs = 200,
                         case = 3,
                         sigma.in = Sigma,
                         gamma.in = gammax,
                         Axx.in = matrix(c(0.3, 0.5, 0.4, 0.3), nrow = 2, ncol = 2),
                         ayxUC.in = c(0.5,0.6),
                         ayy.in = 0.7,
                         mu.in = rep(0.3, 3),
                         eta.in = rep(0, 3),
                         azeroy.in = 0.4,
                         aoney.in = 0,
                         burn.in = 50,
                         seed.in = 10)

bootCT documentation built on Sept. 27, 2022, 5:05 p.m.