# R/LS.norm.R In TAR: Bayesian Modeling of Autoregressive Threshold Time Series Models

#### Documented in LS.norm

#' @import
#' @export
#'
#' @title
#' Estimate a Gaussian TAR model using Least Square method given the structural parameters.
#' @description
#' This function estimate a Gaussian TAR model using Least Square method given the structural parameters, i.e. the number of regimes, thresholds and autoregressive orders.
#' @return
#' The function returns the autoregressive coefficients matrix theta and variance weights \eqn{H}. Rows of the matrix theta represent regimes
#' @details
#' The TAR model is given by \deqn{X_t=a_0^{(j)} + \sum_{i=1}^{k_j}a_i^{(j)}X_{t-i}+h^{(j)}e_t} when \eqn{Z_t\in (r_{j-1},r_j]} for som \eqn{j} (\eqn{j=1,\cdots,l}).
#' the \eqn{\{Z_t\}} is the threshold process, \eqn{l} is the number of regimes, \eqn{k_j} is the autoregressive order in the regime \eqn{j}. \eqn{a_i^{(j)}} with \eqn{i=0,1,\cdots,k_j} denote the autoregressive coefficients, while \eqn{h^{(j)}} denote the variance weights.
#' @author Hanwen Zhang <hanwenzhang at usantotomas.edu.co>
#' @param Z The threshold series
#' @param X The series of interest
#' @param l The number of regimes.
#' @param r The vector of thresholds for the series \eqn{\{Z_t\}}.
#' @param K The vector containing the autoregressive orders of the \eqn{l} regimes.
#'
#'
#' @references
#' Nieto, F. H. (2005), \emph{Modeling Bivariate Threshold Autoregressive Processes in the Presence of Missing Data}. Communications in Statistics. Theory and Methods, 34; 905-930
#' @examples
#' Z<-arima.sim(n=500,list(ar=c(0.5)))
#' l <- 2
#' r <- 0
#' K <- c(2,1)
#' theta <- matrix(c(1,-0.5,0.5,-0.7,-0.3,NA), nrow=l)
#' H <- c(1, 1.5)
#' X <- simu.tar.norm(Z,l,r,K,theta,H)
#' LS.norm(Z,X,l,r,c(0,0))

LS.norm <- function(Z, X, l, r, K){
if(length(r)!=(l-1))
stop("The number of thresholds should be l-1")
if(length(K)!=l)
stop("A TAR model with l regimes should have l autoregressive orders")
N <- length(Z)
J <- rep(l, N)
r <- c(min(Z)-0.1, r)
for(j in 1:l){
J[which(as.double(Z<=r[j+1])-as.double(Z<=r[j])==1)] <- j
}
k <- max(K)
if(k>0){
J.k <- J[-(1:k)]
nj.k <- table(J.k)
}
if(k==0){
J.k <- J
nj.k <- table(J.k)
}

theta.est <- matrix(NA,l,k+1)

for(j in 1:l){
CONT<-nj.k[j]
Y<-matrix(NA,CONT,1)
ZZ<-matrix(NA,CONT,(K[j]+1))
if(K[j]==0){ZZ<-matrix(1,CONT,1)
IN=0
for(ix in (k+1):N){
{ if (J.k[ix-k]==j)
{ IN=IN+1
Y[IN,1]=X[ix]
}
}
}
}
if(K[j]>0){
IN=0
for  (iy in (k+1):N)
{        if (J.k[iy-k]==j)
{ IN=IN+1
Y[IN,1]=X[iy]
ZZ[IN,1]=1
for (ii in (1:K[j])){ZZ[IN,ii+1]=X[iy-ii]}
}
} }
theta.est[j,1:(K[j]+1)] <- solve(t(ZZ)%*%ZZ)%*%t(ZZ)%*%Y}
e<-rep(NA,N)
if(k>0) {
e[1:k]<-0
for(t in (k+1):N){
jt<-J[t]   ### jt es el r?gimen donde est? el t-?simo dato
a<-theta.est[jt,1:(K[jt]+1)]   ### coeficientes autoregresivos para el regimen correspondiente al t-?simo dato
e[t]<-X[t]-a[1]-sum(a[-1]*X[(t-1):(t-K[jt])])
}
}
##########################
if(k==0){
e<-rep(NA,N)
for(t in 1:N){
jt<-J[t]   ### jt es el r?gimen donde est? el t-?simo dato
a<-theta.est[jt,1]   ### coeficientes autoregresivos para el regimen correspondiente al t-?simo dato
e[t]<-X[t]-a
}
}
h.est <- rep(NA,l)
for(ll in 1:l){
h.est[ll] <- sd(e[which(J==ll)])
}
list(theta.est=theta.est,h.est=h.est)
}


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TAR documentation built on May 2, 2019, 3:40 a.m.