R/MDSVsim.R
In Abdoulhaki/MDSV: Multifractal Discrete Stochastic Volatility
Defines functions
MDSVsim
Documented in
MDSVsim
#' @title MDSV Simulation
#' @description Method for simulating from a variety of MDSV model (uniquely or jointly).
#' @param N An integer designing the number of components for the MDSV process
#' @param K An integer designing the number of states of each MDSV process component
#' @param para A vector of parameters use for the MDSV simulation.
#' @param ModelType An integer designing the type of model to be fit. \eqn{0} for univariate log-returns, \eqn{1} for univariate realized variances and \eqn{2} for joint log-return and realized variances.
#' @param LEVIER if \code{TRUE}, estime the MDSV model with leverage.
#' @param n.sim The simulation horizon.
#' @param n.start The burn-in sample.
#' @param m.sim The number of simulations.
#' @param rseed An integer use to initialize the random number generator for the resampling with replacement method (if not supplied take randomly).
#'
#' @return A list consisting of:
#' \itemize{
#' \item ModelType : type of model to be fitted.
#' \item LEVIER : wheter the fit take the leverage effect into account or not.
#' \item N : number of components for the MDSV process.
#' \item K : number of states of each MDSV process component.
#' \item parameters : parameters used for the simulation.
#' \item n.sim : simulation horizon.
#' \item n.start : burn-in sample.
#' \item m.sim : number of simulations.
#' \item r_t : simulated log-returns (only if ModelType == 0 or ModelType == 2).
#' \item RV_t : simulated realized variances (only if ModelType == 1 or ModelType == 2).
#' }
#'
#' @details
#' n.start is the simulation horizon to be delete (from the start). The leverage effect is taken into
#' account according to the FHMV model (see Augustyniak et al., 2019). While simulating an
#' univariate realized variances data, this package does not allow to add leverage effect.
#'
#' @references
#' Augustyniak, M., Bauwens, L., & Dufays, A. (2019). A new approach to volatility modeling: the factorial hidden Markov volatility model.
#' \emph{Journal of Business & Economic Statistics}, 37(4), 696-709. \url{https://doi.org/10.1080/07350015.2017.1415910}
#'
#' @seealso For fitting \code{\link{MDSVfit}}, filtering \code{\link{MDSVfilter}}, bootstrap forecasting \code{\link{MDSVboot}} and rolling estimation and forecast \code{\link{MDSVroll}}.
#'
#' @examples
#' \dontrun{
#' # MDSV(N=2,K=3) without leverage on univariate log-returns S&P500
#' N <- 2 # Number of components
#' K <- 3 # Number of states
#' ModelType <- 0 # Univariate log-returns
#' para <- c(omega = 0.52, a = 0.99, b = 2.77, sigma = 1.95, v0 = 0.72)
#' LEVIER <- FALSE # No leverage effect
#' n.sim <- 2000 # length of the simulation
#' n.start <- 70 # No burn-in
#' m.sim <- 1 # Number of simulation
#'
#' # simulation
#' out <- MDSVsim(K = K, N = N, para = para, ModelType = ModelType, LEVIER = LEVIER, n.sim = n.sim,
#' n.start = n.start, m.sim = m.sim, rseed = NA)
#'
#'
#' # MDSV(N=3,K=3) with leverage on joint log-returns and realized variances NASDAQ
#' N <- 3 # Number of components
#' K <- 3 # Number of states
#' ModelType <- 2 # Univariate log-returns
#' para <- c(omega = 0.52, a = 0.99, b = 2.77, sigma = 1.95, v0 = 0.72,
#' xi = -0.5, varphi = 0.93, delta1 = 0.93, delta2 = 0.04, shape = 2.10,
#' l = 0.78, theta = 0.876)
#' LEVIER <- TRUE # No leverage effect
#' n.sim <- 2000 # length of the simulation
#' n.start <- 500 # No burn-in
#' m.sim <- 3 # Number of simulation
#'
#' # simulation
#' out <- MDSVsim(K = K, N = N, para = para, ModelType = ModelType, LEVIER = LEVIER, n.sim = n.sim,
#' n.start = n.start, m.sim = m.sim, rseed = NA)
#'
#' }
#' @export
#' @importFrom mhsmm sim.mc
MDSVsim<-function(N, K, para, ModelType = 0, LEVIER = FALSE, n.sim = 1000, n.start = 0, m.sim = 1, rseed = NA, dis = "lognormal"){
if ( (!is.numeric(N)) || (!is.numeric(K)) ) {
stop("MDSVsim(): input N and K must all be numeric!")
}else if(!(N%%1==0) || !(K%%1==0)){
stop("MDSVsim(): input N and K must all be integer!")
}else if(K<2){
stop("MDSVfit(): input K must be greater than one!")
}else if(N<1){
stop("MDSVfit(): input N must be positive!")
}
if ( (!is.numeric(n.sim)) || (!is.numeric(n.start)) || (!is.numeric(m.sim))) {
stop("MDSVsim(): input n.sim, n.start and m.sim must all be numeric!")
}else if(!(n.sim%%1==0) || !(n.start%%1==0) || !(m.sim%%1==0)){
stop("MDSVsim(): input n.sim, n.start and m.sim must all be integer!")
}else if((n.sim<1) || (m.sim<1)){
stop("MDSVfit(): input n.sim and m.sim must be positive!")
}
if(n.start<0){
stop("MDSVfit(): input n.start must be positive or 0!")
}
if(!is.numeric(ModelType)) {
stop("MDSVsim(): input ModelType must be numeric!")
}else if(!(ModelType %in% c(0,1,2))){
stop("MDSVsim(): input ModelType must be 0, 1 or 2!")
}
if ((!is.numeric(rseed)) & !is.na(rseed)) {
print("MDSVsim() WARNING: input rseed must be numeric! rseed set to random")
rseed <- sample.int(.Machine$integer.max,1)
}else if(is.numeric(rseed)){
if(!(rseed%%1==0)){
rseed <- floor(rseed)
print(paste0("MDSVsim() WARNING: input rseed must be an integer! rseed set to ",rseed))
}
set.seed(rseed)
}
if(!is.logical(LEVIER)) {
stop("MDSVsim(): input LEVIER must be logical!")
}
if ((ModelType == 1) & LEVIER) {
print("MDSVsim() WARNING: can not simulate univariate realized variance with leverage effect! Set to FALSE")
LEVIER <- FALSE
}
if(LEVIER) n.start <- n.start+70
if(!is.numeric(para)) {
stop("MDSVsim(): input para must be numeric!")
}else if(!is.vector(para)) {
stop("MDSVsim(): input para must be vector!")
}else if(((!LEVIER) & (ModelType==0) & !(length(para)==5)) ||
((!LEVIER) & (ModelType==1) & !(length(para)==6)) ||
((!LEVIER) & (ModelType==2) & !(length(para)==10)) ||
((LEVIER) & (ModelType==0) & !(length(para)==7)) ||
((LEVIER) & (ModelType==1) & !(length(para)==8)) ||
((LEVIER) & (ModelType==2) & !(length(para)==12))){
stop("MDSVsim(): incorrect input para!")
}
if((para[1]>1) || (para[1]<0)) {
stop("MDSVsim(): input para[omega] must be between 0 and 1!")
}else if((para[2]>1) || (para[2]<0)) {
stop("MDSVsim(): input para[a] must be between 0 and 1!")
}else if((para[3]<=1)) {
stop("MDSVsim(): input para[b] must be greater than 1!")
}else if((para[4]<=0)) {
stop("MDSVsim(): input para[sigma] must be greater than 0!")
}else if((para[5]>1) || (para[5]<0)) {
stop("MDSVsim(): input para[v0] must be between 0 and 1!")
}else if((ModelType==1) & (para[6]<=0)) {
stop("MDSVsim(): input para[shape] must be greater than 0!")
}else if((ModelType==2) & (para[10]<=0)){
stop("MDSVsim(): input para[shape] must be greater than 0!")
}else if(LEVIER){
if(ModelType==0){
if(para[6]<=0){
stop("MDSVsim(): input para[l] must be greater than 0!")
}else if((para[7]>1) || (para[7]<0)){
stop("MDSVsim(): input para[theta_l] must be between 0 and 1!")
}
}else if(ModelType==1){
if(para[7]<=0){
stop("MDSVsim(): input para[l] must be greater than 0!")
}else if((para[8]>1) || (para[8]<0)){
stop("MDSVsim(): input para[theta_l] must be between 0 and 1!")
}
}else if(ModelType==2){
if(para[11]<=0){
stop("MDSVsim(): input para[l] must be greater than 0!")
}else if((para[12]>1) || (para[12]<0)){
stop("MDSVsim(): input para[theta_l] must be between 0 and 1!")
}
}
}
vars<-c("omega","a","b","sigma","v0")
if(ModelType==1) vars <- c(vars,"shape")
if(ModelType==2) vars <- c(vars,"xi","varphi","delta1","delta2","shape")
if(LEVIER) vars <- c(vars,"l","theta")
names(para) <- vars
out <- NULL
v <- volatilityVector(para = para, K = K, N = N)
MatrixP <- P(para = para, K = K, N = N)
stationnaryDist <- probapi(omega = para["omega"], K = K, N = N)
V_t <- v[sim.mc(stationnaryDist,MatrixP,n.sim+n.start)]
if(!LEVIER){
for(sim in 1:m.sim){
tmp <- NULL
if(ModelType == 0) {
r_t <- rnorm(n.sim+n.start,0,sqrt(V_t))
r_t <- r_t[(n.start+1):(n.sim+n.start)]
tmp <- list(r_t = r_t)
}else if(ModelType == 2) {
r_t <- rnorm(n.sim+n.start,0,sqrt(V_t))
e_t <- r_t/sqrt(V_t)
RV_t <- exp(para["xi"] + para["varphi"]*log(V_t) + para["delta1"]*e_t + para["delta2"]*(e_t^2-1) + para["shape"]*rnorm(n.sim+n.start))
RV_t <- RV_t[(n.start+1):(n.sim+n.start)]
r_t <- r_t[(n.start+1):(n.sim+n.start)]
tmp <- list(r_t = r_t, RV_t = RV_t)
}else if(ModelType == 1) {
if(dis=="gamma"){
RV_t <- V_t*rgamma(n.sim+n.start,shape = para["shape"], rate = 1/para["shape"])
}else{
RV_t <- V_t*rlnorm(n.sim+n.start,meanlog=-para["shape"]/2, sdlog=sqrt(para["shape"]))
}
RV_t <- RV_t[(n.start+1):(n.sim+n.start)]
tmp <- list(RV_t = RV_t)
}
out <- c(out,list(tmp))
names(out)[sim] <- paste("sim",sim,sep = ".")
}
}else{
for(sim in 1:m.sim){
tmp <- NULL
if(ModelType == 0) {
r_t <- rnorm(70,0,sqrt(V_t[1:70]))
for(t in 1:(n.sim+n.start)){
lt <- levierVolatility(ech = r_t, para = para, Model_type = ModelType)$levier
r_t <- c(r_t, rnorm(1,0,sqrt(lt*V_t[70+t])))
}
r_t <- r_t[(n.start+1):(n.sim+n.start)]
tmp <- list(r_t = r_t)
}else if(ModelType == 2) {
r_t <- rnorm(70,0,sqrt(V_t[1:70]))
e_t <- r_t/sqrt(V_t[1:70])
for(t in 1:(n.sim+n.start-70)){
lt <- levierVolatility(ech = r_t, para = para, Model_type = ModelType)$levier
r_t <- c(r_t, rnorm(1,0,sqrt(lt*V_t[70+t])))
e_t <- c(e_t,r_t[t]/sqrt(lt*V_t[70+t]))
}
RV_t <- exp(para["xi"] + para["varphi"]*log(V_t) + para["delta1"]*e_t + para["delta2"]*(e_t^2-1) + para["shape"]*rnorm(n.sim+n.start))
RV_t <- RV_t[(n.start+1):(n.sim+n.start)]
r_t <- r_t[(n.start+1):(n.sim+n.start)]
tmp <- list(r_t = r_t, RV_t = RV_t)
}
out <- c(out,list(tmp))
names(out)[sim] <- paste("sim",sim,sep = ".")
}
}
if(ModelType==0) Model_type <- "Univariate log-return"
if(ModelType==1) Model_type <- "Univariate realized variances"
if(ModelType==2) Model_type <- "Joint log-return and realized variances"
out<-c(list(ModelType = Model_type,
LEVIER = LEVIER,
N = N,
K = K,
parameters = para,
n.sim = n.sim,
n.start = n.start,
m.sim = m.sim),
out)
class(out) <- "MDSVsim"
return(out)
}
Abdoulhaki/MDSV documentation built on July 6, 2024, 4:03 p.m.
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Defines functions MDSVsim
Documented in MDSVsim
#' @title MDSV Simulation
#' @description Method for simulating from a variety of MDSV model (uniquely or jointly).
#' @param N An integer designing the number of components for the MDSV process
#' @param K An integer designing the number of states of each MDSV process component
#' @param para A vector of parameters use for the MDSV simulation.
#' @param ModelType An integer designing the type of model to be fit. \eqn{0} for univariate log-returns, \eqn{1} for univariate realized variances and \eqn{2} for joint log-return and realized variances.
#' @param LEVIER if \code{TRUE}, estime the MDSV model with leverage.
#' @param n.sim The simulation horizon.
#' @param n.start The burn-in sample.
#' @param m.sim The number of simulations.
#' @param rseed An integer use to initialize the random number generator for the resampling with replacement method (if not supplied take randomly).
#'
#' @return A list consisting of:
#' \itemize{
#' \item ModelType : type of model to be fitted.
#' \item LEVIER : wheter the fit take the leverage effect into account or not.
#' \item N : number of components for the MDSV process.
#' \item K : number of states of each MDSV process component.
#' \item parameters : parameters used for the simulation.
#' \item n.sim : simulation horizon.
#' \item n.start : burn-in sample.
#' \item m.sim : number of simulations.
#' \item r_t : simulated log-returns (only if ModelType == 0 or ModelType == 2).
#' \item RV_t : simulated realized variances (only if ModelType == 1 or ModelType == 2).
#' }
#'
#' @details
#' n.start is the simulation horizon to be delete (from the start). The leverage effect is taken into
#' account according to the FHMV model (see Augustyniak et al., 2019). While simulating an
#' univariate realized variances data, this package does not allow to add leverage effect.
#'
#' @references
#' Augustyniak, M., Bauwens, L., & Dufays, A. (2019). A new approach to volatility modeling: the factorial hidden Markov volatility model.
#' \emph{Journal of Business & Economic Statistics}, 37(4), 696-709. \url{https://doi.org/10.1080/07350015.2017.1415910}
#'
#' @seealso For fitting \code{\link{MDSVfit}}, filtering \code{\link{MDSVfilter}}, bootstrap forecasting \code{\link{MDSVboot}} and rolling estimation and forecast \code{\link{MDSVroll}}.
#'
#' @examples
#' \dontrun{
#' # MDSV(N=2,K=3) without leverage on univariate log-returns S&P500
#' N <- 2 # Number of components
#' K <- 3 # Number of states
#' ModelType <- 0 # Univariate log-returns
#' para <- c(omega = 0.52, a = 0.99, b = 2.77, sigma = 1.95, v0 = 0.72)
#' LEVIER <- FALSE # No leverage effect
#' n.sim <- 2000 # length of the simulation
#' n.start <- 70 # No burn-in
#' m.sim <- 1 # Number of simulation
#'
#' # simulation
#' out <- MDSVsim(K = K, N = N, para = para, ModelType = ModelType, LEVIER = LEVIER, n.sim = n.sim,
#' n.start = n.start, m.sim = m.sim, rseed = NA)
#'
#'
#' # MDSV(N=3,K=3) with leverage on joint log-returns and realized variances NASDAQ
#' N <- 3 # Number of components
#' K <- 3 # Number of states
#' ModelType <- 2 # Univariate log-returns
#' para <- c(omega = 0.52, a = 0.99, b = 2.77, sigma = 1.95, v0 = 0.72,
#' xi = -0.5, varphi = 0.93, delta1 = 0.93, delta2 = 0.04, shape = 2.10,
#' l = 0.78, theta = 0.876)
#' LEVIER <- TRUE # No leverage effect
#' n.sim <- 2000 # length of the simulation
#' n.start <- 500 # No burn-in
#' m.sim <- 3 # Number of simulation
#'
#' # simulation
#' out <- MDSVsim(K = K, N = N, para = para, ModelType = ModelType, LEVIER = LEVIER, n.sim = n.sim,
#' n.start = n.start, m.sim = m.sim, rseed = NA)
#'
#' }
#' @export
#' @importFrom mhsmm sim.mc
MDSVsim<-function(N, K, para, ModelType = 0, LEVIER = FALSE, n.sim = 1000, n.start = 0, m.sim = 1, rseed = NA, dis = "lognormal"){
if ( (!is.numeric(N)) || (!is.numeric(K)) ) {
stop("MDSVsim(): input N and K must all be numeric!")
}else if(!(N%%1==0) || !(K%%1==0)){
stop("MDSVsim(): input N and K must all be integer!")
}else if(K<2){
stop("MDSVfit(): input K must be greater than one!")
}else if(N<1){
stop("MDSVfit(): input N must be positive!")
}
if ( (!is.numeric(n.sim)) || (!is.numeric(n.start)) || (!is.numeric(m.sim))) {
stop("MDSVsim(): input n.sim, n.start and m.sim must all be numeric!")
}else if(!(n.sim%%1==0) || !(n.start%%1==0) || !(m.sim%%1==0)){
stop("MDSVsim(): input n.sim, n.start and m.sim must all be integer!")
}else if((n.sim<1) || (m.sim<1)){
stop("MDSVfit(): input n.sim and m.sim must be positive!")
}
if(n.start<0){
stop("MDSVfit(): input n.start must be positive or 0!")
}
if(!is.numeric(ModelType)) {
stop("MDSVsim(): input ModelType must be numeric!")
}else if(!(ModelType %in% c(0,1,2))){
stop("MDSVsim(): input ModelType must be 0, 1 or 2!")
}
if ((!is.numeric(rseed)) & !is.na(rseed)) {
print("MDSVsim() WARNING: input rseed must be numeric! rseed set to random")
rseed <- sample.int(.Machine$integer.max,1)
}else if(is.numeric(rseed)){
if(!(rseed%%1==0)){
rseed <- floor(rseed)
print(paste0("MDSVsim() WARNING: input rseed must be an integer! rseed set to ",rseed))
}
set.seed(rseed)
}
if(!is.logical(LEVIER)) {
stop("MDSVsim(): input LEVIER must be logical!")
}
if ((ModelType == 1) & LEVIER) {
print("MDSVsim() WARNING: can not simulate univariate realized variance with leverage effect! Set to FALSE")
LEVIER <- FALSE
}
if(LEVIER) n.start <- n.start+70
if(!is.numeric(para)) {
stop("MDSVsim(): input para must be numeric!")
}else if(!is.vector(para)) {
stop("MDSVsim(): input para must be vector!")
}else if(((!LEVIER) & (ModelType==0) & !(length(para)==5)) ||
((!LEVIER) & (ModelType==1) & !(length(para)==6)) ||
((!LEVIER) & (ModelType==2) & !(length(para)==10)) ||
((LEVIER) & (ModelType==0) & !(length(para)==7)) ||
((LEVIER) & (ModelType==1) & !(length(para)==8)) ||
((LEVIER) & (ModelType==2) & !(length(para)==12))){
stop("MDSVsim(): incorrect input para!")
}
if((para[1]>1) || (para[1]<0)) {
stop("MDSVsim(): input para[omega] must be between 0 and 1!")
}else if((para[2]>1) || (para[2]<0)) {
stop("MDSVsim(): input para[a] must be between 0 and 1!")
}else if((para[3]<=1)) {
stop("MDSVsim(): input para[b] must be greater than 1!")
}else if((para[4]<=0)) {
stop("MDSVsim(): input para[sigma] must be greater than 0!")
}else if((para[5]>1) || (para[5]<0)) {
stop("MDSVsim(): input para[v0] must be between 0 and 1!")
}else if((ModelType==1) & (para[6]<=0)) {
stop("MDSVsim(): input para[shape] must be greater than 0!")
}else if((ModelType==2) & (para[10]<=0)){
stop("MDSVsim(): input para[shape] must be greater than 0!")
}else if(LEVIER){
if(ModelType==0){
if(para[6]<=0){
stop("MDSVsim(): input para[l] must be greater than 0!")
}else if((para[7]>1) || (para[7]<0)){
stop("MDSVsim(): input para[theta_l] must be between 0 and 1!")
}
}else if(ModelType==1){
if(para[7]<=0){
stop("MDSVsim(): input para[l] must be greater than 0!")
}else if((para[8]>1) || (para[8]<0)){
stop("MDSVsim(): input para[theta_l] must be between 0 and 1!")
}
}else if(ModelType==2){
if(para[11]<=0){
stop("MDSVsim(): input para[l] must be greater than 0!")
}else if((para[12]>1) || (para[12]<0)){
stop("MDSVsim(): input para[theta_l] must be between 0 and 1!")
}
}
}
vars<-c("omega","a","b","sigma","v0")
if(ModelType==1) vars <- c(vars,"shape")
if(ModelType==2) vars <- c(vars,"xi","varphi","delta1","delta2","shape")
if(LEVIER) vars <- c(vars,"l","theta")
names(para) <- vars
out <- NULL
v <- volatilityVector(para = para, K = K, N = N)
MatrixP <- P(para = para, K = K, N = N)
stationnaryDist <- probapi(omega = para["omega"], K = K, N = N)
V_t <- v[sim.mc(stationnaryDist,MatrixP,n.sim+n.start)]
if(!LEVIER){
for(sim in 1:m.sim){
tmp <- NULL
if(ModelType == 0) {
r_t <- rnorm(n.sim+n.start,0,sqrt(V_t))
r_t <- r_t[(n.start+1):(n.sim+n.start)]
tmp <- list(r_t = r_t)
}else if(ModelType == 2) {
r_t <- rnorm(n.sim+n.start,0,sqrt(V_t))
e_t <- r_t/sqrt(V_t)
RV_t <- exp(para["xi"] + para["varphi"]*log(V_t) + para["delta1"]*e_t + para["delta2"]*(e_t^2-1) + para["shape"]*rnorm(n.sim+n.start))
RV_t <- RV_t[(n.start+1):(n.sim+n.start)]
r_t <- r_t[(n.start+1):(n.sim+n.start)]
tmp <- list(r_t = r_t, RV_t = RV_t)
}else if(ModelType == 1) {
if(dis=="gamma"){
RV_t <- V_t*rgamma(n.sim+n.start,shape = para["shape"], rate = 1/para["shape"])
}else{
RV_t <- V_t*rlnorm(n.sim+n.start,meanlog=-para["shape"]/2, sdlog=sqrt(para["shape"]))
}
RV_t <- RV_t[(n.start+1):(n.sim+n.start)]
tmp <- list(RV_t = RV_t)
}
out <- c(out,list(tmp))
names(out)[sim] <- paste("sim",sim,sep = ".")
}
}else{
for(sim in 1:m.sim){
tmp <- NULL
if(ModelType == 0) {
r_t <- rnorm(70,0,sqrt(V_t[1:70]))
for(t in 1:(n.sim+n.start)){
lt <- levierVolatility(ech = r_t, para = para, Model_type = ModelType)$levier
r_t <- c(r_t, rnorm(1,0,sqrt(lt*V_t[70+t])))
}
r_t <- r_t[(n.start+1):(n.sim+n.start)]
tmp <- list(r_t = r_t)
}else if(ModelType == 2) {
r_t <- rnorm(70,0,sqrt(V_t[1:70]))
e_t <- r_t/sqrt(V_t[1:70])
for(t in 1:(n.sim+n.start-70)){
lt <- levierVolatility(ech = r_t, para = para, Model_type = ModelType)$levier
r_t <- c(r_t, rnorm(1,0,sqrt(lt*V_t[70+t])))
e_t <- c(e_t,r_t[t]/sqrt(lt*V_t[70+t]))
}
RV_t <- exp(para["xi"] + para["varphi"]*log(V_t) + para["delta1"]*e_t + para["delta2"]*(e_t^2-1) + para["shape"]*rnorm(n.sim+n.start))
RV_t <- RV_t[(n.start+1):(n.sim+n.start)]
r_t <- r_t[(n.start+1):(n.sim+n.start)]
tmp <- list(r_t = r_t, RV_t = RV_t)
}
out <- c(out,list(tmp))
names(out)[sim] <- paste("sim",sim,sep = ".")
}
}
if(ModelType==0) Model_type <- "Univariate log-return"
if(ModelType==1) Model_type <- "Univariate realized variances"
if(ModelType==2) Model_type <- "Joint log-return and realized variances"
out<-c(list(ModelType = Model_type,
LEVIER = LEVIER,
N = N,
K = K,
parameters = para,
n.sim = n.sim,
n.start = n.start,
m.sim = m.sim),
out)
class(out) <- "MDSVsim"
return(out)
}
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