sim_vecm_ardl {bootCT}

Generate data from a VECM/ARDL equation

Description

Generate data from a VECM/ARDL equation

Usage

sim_vecm_ardl(
  nobs,
  case = 1,
  sigma.in,
  gamma.in,
  axx.in,
  ayx.uc.in,
  ayy.in,
  mu.in = NULL,
  eta.in = NULL,
  azero.in = NULL,
  aone.in = NULL,
  burn.in = nobs * 0.5,
  seed.in = NULL
)

Arguments

nobs

number of observations.

case

case related to intercept and trend

sigma.in

error covariance matrix \boldsymbol\Sigma

gamma.in

list of VECM short-run parameter matrices \boldsymbol\Gamma_j

axx.in

long-run relationships between the independent variables \mathbf A_{xx}

ayx.uc.in

long-run unconditional relationship between dependent and independent variables, \mathbf a_{yx}. The second component ayxC, derived from conditioning, is calculated as \mathbf a_{yx}^{(C)}= - \boldsymbol\omega'\mathbf A_{xx}

ayy.in

long-run relationship for the dependent variable a_{yy}

mu.in

VAR intercept vector \boldsymbol\mu (CASE II)

eta.in

VAR trend vector \boldsymbol\eta (CASE IV)

azero.in

VECM intercept \boldsymbol{\alpha}_{0} (CASE III-IV-V)

aone.in

VECM trend \boldsymbol{\alpha}_{1} (CASE V)

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 \boldsymbol\Sigma.

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

• at: the conditional long-run parameter matrix \widetilde{\mathbf A}

• ayy: the coefficient weighting the EC term, a_{yy}

• ayx.uc: the unconditional subvector of the ARDL equation \mathbf a_{yx}

• ayx2: the conditioning effect \omega'A_{xx}

• ayx.c: the conditional subvector of the ARDL equation \widetilde{a}_{y.x}=a_{yx}-\omega'A_{xx}

• gammalist: the list of unconditional \boldsymbol\Gamma_j parameter matrices

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

• vmu: the VAR intercept \boldsymbol\mu

• veta: the VAR trend \boldsymbol\eta

• azero: the unconditional VECM intercept \boldsymbol\alpha_0

• aone: the unconditional VECM trend \boldsymbol\alpha_1

• azero.c: the conditional VECM intercept \boldsymbol\alpha_0^c

• aone.c: the conditional VECM trend \boldsymbol\alpha_1^c

• interc.ardl: the conditional ARDL intercept \alpha_{0.y} (case > 2)

• trend.ardl: the conditional ARDL trend \alpha_{1.y} (case = 5)

• theta0: the \theta_0 coefficient in the EC term (case = 2)

• theta1: the \theta_1 coefficient in the EC term (case = 4)

• interc.ec: the conditional ARDL intercept derived from the EC tem \alpha^{EC}_{0.y} (case = 2)

• trend.ec: the conditional ARDL trend derived from the EC tem \alpha^{EC}_{1.y} (case = 4)

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
corrs = (corrm + t(corrm)) + diag(3)
sds = diag(c(1.3, 1.2, 1))
sigma = (sds %*% corrs %*% 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),
                         ayx.uc.in = c(0.5,0.6),
                         ayy.in = 0.7,
                         mu.in = rep(0, 3),
                         eta.in = rep(0, 3),
                         azero.in = rep(0.4, 3),
                         aone.in = rep(0, 3),
                         burn.in = 50,
                         seed.in = 10)