Nothing
R/builtin-gmmGmm.R
In fBasics: Rmetrics - Markets and Basic Statistics
Defines functions
.lintest
.summary.gmm
.bwAndrews2
.weightsAndrews2
.HAC
.gmm
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA
################################################################################
# FUNCTION:
# .gmm
# .HAC
# .weightsAndrews2
# .bwAndrews2
# .summary.gmm
# .lintest
################################################################################
# Code borrowed from
# R's contributed package "gmm" written by Pierre Chausse.
# Rmetrics:
# Note that gmm is not available on Debian as of 2009-04-28.
# To run these functions under Debian/Rmetrics we have them
# implemented here as a builtin.
# We also made modifications for tailored usage with Rmetrics.
# Note that the dependences in the original package requires zoo
# which may create conflicts with Rmetrics timeDate/timeSeries.
# Package: gmm
# Version: 1.0-4
# Date: 2009-03-10
# Title: Generalized Method of Moments and Generalized Empirical Likelihood
# Author: Pierre Chausse <pierre.chausse@uqam.ca>
# Maintainer: Pierre Chausse <pierre.chausse@uqam.ca>
# Description: It is a complete suite to estimate models based on moment
# conditions. It includes the two step Generalized method of moments
# (GMM) of Hansen(1982), the iterated GMM and continuous updated
# estimator (CUE) of Hansen-Eaton-Yaron(1996) and several methods that
# belong to the Generalized Empirical Likelihood (GEL) family of estimators,
# as presented by Smith(1997), Kitamura(1997), Newey-Smith(2004) and
# Anatolyev(2005).
# Depends: R (>= 2.0.0), sandwich, tseries, mvtnorm
# Imports: stats
# License: GPL (>= 2)
# ------------------------------------------------------------------------------
.gmm <-
function(g, x, t0=NULL, gradv=NULL, type=c("twoStep","cue","iterative"),
wmatrix = c("optimal","ident"), vcov=c("HAC","iid"),
kernel=c("Quadratic Spectral","Truncated", "Bartlett", "Parzen",
"Tukey-Hanning"),crit=10e-7,bw = .bwAndrews2,
prewhite = FALSE, ar.method = "ols", approx="AR(1)",tol = 1e-7,
itermax=100,intercept=TRUE,optfct=c("optim","optimize"), ...)
{
type <- match.arg(type)
kernel <- match.arg(kernel)
vcov <- match.arg(vcov)
wmatrix <- match.arg(wmatrix)
optfct <- match.arg(optfct)
typeg=0
if (is(g,"formula"))
{
typeg=1
dat <- .get_dat(g,x,intercept=intercept)
x <- dat$x
g <- function(tet,x,ny=dat$ny,nh=dat$nh,k=dat$k)
{
tet <- matrix(tet,ncol=k)
if (intercept)
{
e <- x[,1:ny] - x[,(ny+1):(ny+k)]%*%t(tet)
gt <- e
for (i in 2:nh)
{
gt <- cbind(gt,e*x[,(ny+k+i)])
}
}
if (!intercept)
e <- x[,1:ny] - x[,(ny+1):(ny+k)]%*%t(tet)
gt <- e*x[,ny+k+1]
if (nh > 1)
{
for (i in 2:nh)
{
gt <- cbind(gt,e*x[,(ny+k+i)])
}
}
return(gt)
}
gradv <- function(x,ny=dat$ny,nh=dat$nh,k=dat$k)
{
dgb <- -(t(x[,(ny+k+1):(ny+k+nh)])%*%x[,(ny+1):(ny+k)])%x%
diag(rep(1,ny))/nrow(x)
return(dgb)
}
tetlin <- function(x,w,ny=dat$ny,nh=dat$nh,k=dat$k)
{
n <- nrow(x)
ym <- as.matrix(x[,1:ny])
xm <- as.matrix(x[,(ny+1):(ny+k)])
hm <- as.matrix(x[,(ny+k+1):(ny+k+nh)])
whx <- solve(w,(crossprod(hm,xm)%x%diag(ny)))
wvecyh <- solve(w,matrix(crossprod(ym,hm),ncol=1))
dg <- gradv(x)
xx <- crossprod(dg,whx)
par <- solve(xx,crossprod(dg,wvecyh))
gb <- matrix(colSums(g(par,x))/n,ncol=1)
value <- crossprod(gb,solve(w,gb))
res <- list(par=par,value=value)
return(res)
}
}
if (optfct == "optimize")
{
n = nrow(g(t0[1],x))
q = ncol(g(t0[1],x))
k = 1
k2 <- k
df <- q-k
}
else
{
if (typeg)
{
k <- dat$k
k2 <- k*dat$ny
n <- nrow(x)
q <- dat$ny*dat$nh
df <- q-k*dat$ny
}
else
{
n = nrow(g(t0,x))
q = ncol(g(t0,x))
k = length(t0)
k2 <- k
df <- q-k
}
}
obj1 <- function(thet)
{
gt <- g(thet,x)
gbar <- as.vector(colMeans(gt))
obj <- crossprod(gbar,solve(w,gbar))
return(obj)
}
iid <- function(thet)
{
gt <- g(thet,x)
v <- crossprod(gt,gt)/n
return(v)
}
Gf <- function(thet)
{
myenv <- new.env()
assign('x',x,envir=myenv)
assign('thet',thet,envir=myenv)
barg <- function(x,thet)
{
gt <- g(thet,x)
gbar <- as.vector(colMeans(gt))
return(gbar)
}
G <- attr(numericDeriv(quote(barg(x,thet)),"thet",myenv),"gradient")
return(G)
}
if (q == k2 | wmatrix == "ident")
{
if (typeg)
{
w <- diag(q)
res <- tetlin(x,w)
z = list(par=res$par,objective=res$value)
}
else
{
w=diag(rep(1,q))
if (optfct == "optim")
res <- optim(t0,obj1, ...)
else
{
res <- optimize(obj1,t0, ...)
res$par <- res$minimum
res$value <- res$objective
}
z = list(par=res$par,objective=res$value)
}
}
else
{
if (type=="twoStep")
{
w=diag(rep(1,q))
if (typeg)
{
res1 <- tetlin(x,w)
}
else
{
if (optfct == "optim")
res1 <- optim(t0,obj1, ...)
else
{
res1 <- optimize(obj1,t0, ...)
res1$par <- res1$minimum
res1$value <- res1$objective
}
}
if (vcov == "iid")
w <- iid(res1$par)
if (vcov == "HAC")
w <- .HAC(g(res1$par,x), kernel=kernel, bw=bw,
prewhite=prewhite,ar.method=ar.method,approx=approx,tol=tol)
if (typeg)
{
res2 <- tetlin(x,w)
}
else
{
if (optfct == "optim")
res2 <- optim(res1$par,obj1, ...)
else
{
res2 <- optimize(obj1,t0, ...)
res2$par <- res2$minimum
res2$value <- res2$objective
}
}
z = list(par=res2$par,objective=res2$value)
}
if (type=="cue")
{
obj_cue <- function(thet)
{
gt <- g(thet,x)
gbar <- as.vector(colMeans(gt))
if (vcov == "iid")
w2 <- iid(thet)
if (vcov == "HAC")
w2 <- .HAC(g(thet,x), kernel=kernel, bw=bw,
prewhite=prewhite,ar.method=ar.method,approx=approx,tol=tol)
obj <- crossprod(gbar,solve(w2,gbar))
return(obj)
}
if (typeg)
{
if (is.null(t0))
t0 <- tetlin(x,diag(rep(1,q)))$par
if (optfct == "optim")
{
res2 <- optim(t0,obj_cue, ...)
}
else
{
res2 <- optimize(obj_cue,t0, ...)
res2$par <- res2$minimum
res2$value <- res2$objective
}
}
else
{
if (optfct == "optim")
res2 <- optim(t0,obj_cue, ...)
else
{
res2 <- optimize(obj_cue,t0, ...)
res2$par <- res2$minimum
res2$value <- res2$objective
}
}
z = list(par=res2$par,objective=res2$value)
}
if (type=="iterative")
{
w=diag(rep(1,q))
if (typeg)
res <- tetlin(x,w)
else
{
if (optfct == "optim")
res <- optim(t0,obj1, ...)
else
{
res <- optimize(obj1,t0, ...)
res$par <- res$minimum
res$value <- res$objective
}
}
ch <- 100000
j <- 1
while(ch>crit)
{
tet <- res$par
if (vcov == "iid")
w2 <- iid(tet)
if (vcov == "HAC")
w2 <- .HAC(g(tet,x), kernel=kernel, bw=bw,
prewhite=prewhite,ar.method=ar.method,approx=approx,tol=tol)
if (typeg)
res <- tetlin(x,w2)
else
{
if (optfct == "optim")
res <- optim(tet,obj1, ...)
else
{
res <- optimize(obj1,t0, ...)
res$par <- res$minimum
res$value <- res$objective
}
}
ch <- crossprod(abs(tet-res$par)/tet,abs(tet-res$par)/tet)
if (j>itermax)
{
cat("No convergence after ",itermax," iterations")
ch <- crit
}
j <- j+1
}
z = list(par=res$par,objective=res$value)
}
}
if (!is.function(gradv))
G <- Gf(z$par)
else
if (typeg)
G <- gradv(x)
else
G <- gradv(z$par,x)
if (vcov == "iid")
v <- iid(z$par)/n
else
v <- .HAC(g(z$par,x), kernel=kernel, bw=bw,prewhite=prewhite,
ar.method=ar.method,approx=approx,tol=tol)/n
if (wmatrix == "optimal")
{
z$vcov <- solve(crossprod(G,solve(v,G)))
}
else
{
GGG <- solve(crossprod(G),t(G))
z$vcov <- GGG%*%v%*%t(GGG)
}
z$gt <- g(z$par,x)
if (typeg==0)
names(z$par) <- paste("Theta[",1:k,"]",sep="")
if (typeg == 1)
{
namex <- colnames(dat$x[,(dat$ny+1):(dat$ny+dat$k)])
nameh <- colnames(dat$x[,(dat$ny+dat$k+1):(dat$ny+dat$k+dat$nh)])
if (dat$ny > 1)
{
namey <- colnames(dat$x[,1:dat$ny])
names(z$par) <- paste(rep(namey,dat$k),"_",rep(namex,rep(dat$ny,dat$k)),sep="")
colnames(z$gt) <- paste(rep(namey,dat$nh),"_",rep(nameh,rep(dat$ny,dat$nh)),sep="")
}
if (dat$ny == 1)
{
names(z$par) <- namex
colnames(z$gt) <- nameh
}
}
dimnames(z$vcov) <- list(names(z$par),names(z$par))
z$df <- df
z$k <- k
z$n <- n
z$met <- type
z$kernel <- kernel
class(z) <- "gmm"
z
}
# ------------------------------------------------------------------------------
.HAC <-
function(x, weights = .weightsAndrews2, bw = .bwAndrews2,
prewhite = FALSE, ar.method = "ols", kernel=c("Quadratic Spectral",
"Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), approx="AR(1)",
tol = 1e-7)
{
n.orig <- n <- nrow(x)
k <- ncol(x)
kernel=match.arg(kernel)
if(prewhite > 0)
{
var.fit <- ar(x, order.max = prewhite, demean = FALSE, aic = FALSE,
method = ar.method)
if(k > 1) D <- solve(diag(ncol(x)) - apply(var.fit$ar, 2:3, sum))
else D <- as.matrix(1/(1 - sum(var.fit$ar)))
x <- as.matrix(na.omit(var.fit$resid))
n <- n - prewhite
}
weights <- weights(x, ar.method = ar.method,kernel=kernel,bw=bw,
approx = approx, prewhite = 1, tol = tol)
if (length(weights) > n)
{
warning("more weights than observations, only first n used")
weights <- weights[1:n]
}
utu <- 0.5 * crossprod(x) * weights[1]
wsum <- n * weights[1]/2
w2sum <- n * weights[1]^2/2
if (length(weights) > 1) {
for (ii in 2:length(weights)) {
utu <- utu + weights[ii] * crossprod(x[1:(n -
ii + 1), , drop = FALSE], x[ii:n, , drop = FALSE])
wsum <- wsum + (n - ii + 1) * weights[ii]
w2sum <- w2sum + (n - ii + 1) * weights[ii]^2
}
}
utu <- utu + t(utu)
if(prewhite > 0) {
utu <- crossprod(t(D), utu) %*% t(D)
}
wsum <- 2 * wsum
w2sum <- 2 * w2sum
bc <- n^2/(n^2 - wsum)
df <- n^2/w2sum
rval <- utu/n.orig
return(rval)
}
# ------------------------------------------------------------------------------
.weightsAndrews2 <-
function(x, bw = .bwAndrews2, kernel = c("Quadratic Spectral",
"Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), approx = c("AR(1)",
"ARMA(1,1)"), prewhite = 1, ar.method = "ols", tol = 1e-7, verbose = FALSE)
{
kernel <- match.arg(kernel)
approx=match.arg(approx)
if (is.function(bw))
bw <- bw(x, kernel = kernel, prewhite = prewhite,
ar.method = ar.method, approx=approx)
n <- NROW(x)
weights <- .kweights(0:(n - 1)/bw, kernel = kernel)
weights <- weights[1:max(which(abs(weights) > tol))]
return(weights)
}
# ------------------------------------------------------------------------------
.bwAndrews2 <-
function(x, kernel = c("Quadratic Spectral",
"Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), approx = c("AR(1)",
"ARMA(1,1)"), prewhite = 1, ar.method = "ols")
{
kernel <- match.arg(kernel)
approx <- match.arg(approx)
n <- nrow(x)
k <- ncol(x)
if (approx == "AR(1)") {
fitAR1 <- function(x) {
rval <- ar(x, order.max = 1, aic = FALSE, method = "ols")
rval <- c(rval$ar, sqrt(rval$var.pred))
names(rval) <- c("rho", "sigma")
return(rval)
}
ar.coef <- apply(x, 2, fitAR1)
denum <- sum((ar.coef["sigma", ]/(1 - ar.coef["rho",
]))^4)
alpha2 <- sum(4 * ar.coef["rho", ]^2 * ar.coef["sigma",
]^4/(1 - ar.coef["rho", ])^8)/denum
alpha1 <- sum(4 * ar.coef["rho", ]^2 * ar.coef["sigma",
]^4/((1 - ar.coef["rho", ])^6 * (1 + ar.coef["rho",
])^2))/denum
}
else {
fitARMA11 <- function(x) {
rval <- arima(x, order = c(1, 0, 1), include.mean = FALSE)
rval <- c(rval$coef, sqrt(rval$sigma2))
names(rval) <- c("rho", "psi", "sigma")
return(rval)
}
arma.coef <- apply(x, 2, fitARMA11)
denum <- sum(((1 + arma.coef["psi", ]) * arma.coef["sigma",
]/(1 - arma.coef["rho", ]))^4)
alpha2 <- sum(4 * ((1 + arma.coef["rho", ] *
arma.coef["psi", ]) * (arma.coef["rho", ] + arma.coef["psi",
]))^2 * arma.coef["sigma", ]^4/(1 - arma.coef["rho",
])^8)/denum
alpha1 <- sum(4 * ((1 + arma.coef["rho", ] *
arma.coef["psi", ]) * (arma.coef["rho", ] + arma.coef["psi",
]))^2 * arma.coef["sigma", ]^4/((1 - arma.coef["rho",
])^6 * (1 + arma.coef["rho", ])^2))/denum
}
rval <- switch(kernel, Truncated = {
0.6611 * (n * alpha2)^(1/5)
}, Bartlett = {
1.1447 * (n * alpha1)^(1/3)
}, Parzen = {
2.6614 * (n * alpha2)^(1/5)
}, "Tukey-Hanning" = {
1.7462 * (n * alpha2)^(1/5)
}, "Quadratic Spectral" = {
1.3221 * (n * alpha2)^(1/5)
})
return(rval)
}
# ------------------------------------------------------------------------------
.summary.gmm <-
function(object, interval=FALSE, ...)
{
z <- object
se <- sqrt(diag(z$vcov))
par <- z$par
tval <- par/se
j <- z$objective*z$n
ans <- list(met=z$met,kernel=z$kernel,algo=z$algo)
names(ans$met) <- "GMM method"
names(ans$kernel) <- "kernel for cov matrix"
ans$par <- round(cbind(par,se, tval, 2 * pnorm(abs(tval), lower.tail = FALSE)),5)
dimnames(ans$par) <- list(names(z$par),
c("Estimate", "Std. Error", "t value", "Pr(>|t|)"))
ans$J_test <- noquote(paste("Test-J degrees of freedom is ",z$df,sep=""))
ans$j <- noquote(cbind(j,ifelse(z$df>0,pchisq(j,z$df,lower.tail = FALSE),"*******")))
dimnames(ans$j) <- list("Test E(g)=0: ",c("J-test","Pz(>j)"))
if (interval != FALSE)
{
zs <- qnorm((1-interval)/2,lower.tail=FALSE)
ch <- zs*se
ans$interval <- cbind(par-ch,par+ch)
dimnames(ans$interval) <- list(names(par),c("Theta_lower","Theta_upper"))
}
class(ans) <- "summary.gmm"
ans
}
# ------------------------------------------------------------------------------
.lintest <-
function(object,R,c)
{
z <- object
dl <- nrow(R)
rest <- R%*%z$par - c
vcov_par <- if (inherits(z, "gmm")) z$vcov else z$vcov_par
vcov <- R%*%vcov_par%*%t(R)
h0 <- matrix(rep(NA,nrow(R)),ncol=1)
for (i in 1:nrow(R))
{
testnames <- names(z$par)[R[i,]!=0]
rn <- R[i,][R[i,]!=0]
if (rn[1] != 1)
h0[i] <- paste(rn[1],"*",testnames[1],sep="")
else
h0[i] <- testnames[1]
if (length(rn) > 1)
{
for (j in 2:length(rn))
{
if (rn[j] >= 0)
{
if (rn[j] != 1)
h0[i] <- paste(h0[i]," + ",rn[j],"*",testnames[j],sep="")
else
h0[i] <- paste(h0[i]," + ",testnames[j],sep="")
}
else
{
if (abs(rn[j]) != 1)
h0[i] <- paste(h0[i]," - ",abs(rn[j]),"*",testnames[j],sep="")
else
h0[i] <- paste(h0[i]," - ",testnames[j],sep="")
}
}
}
h0[i] <- paste(h0[i]," = ",c[i],sep="")
}
rh <- solve(vcov,rest)
ans <- list(description <- "Wald test for H0: R(Theta)=c")
ans$H0 <- noquote(h0)
colnames(ans$H0) <- "Null Hypothesis"
wt <- crossprod(rest,rh)
pv <- pchisq(wt,dl,lower.tail=FALSE)
res <- cbind(wt,pv)
dimnames(res) <- list("Wald test", c("Statistics","P-Value"))
ans$result <- res
ans
}
################################################################################
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Defines functions .lintest .summary.gmm .bwAndrews2 .weightsAndrews2 .HAC .gmm
# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA
################################################################################
# FUNCTION:
# .gmm
# .HAC
# .weightsAndrews2
# .bwAndrews2
# .summary.gmm
# .lintest
################################################################################
# Code borrowed from
# R's contributed package "gmm" written by Pierre Chausse.
# Rmetrics:
# Note that gmm is not available on Debian as of 2009-04-28.
# To run these functions under Debian/Rmetrics we have them
# implemented here as a builtin.
# We also made modifications for tailored usage with Rmetrics.
# Note that the dependences in the original package requires zoo
# which may create conflicts with Rmetrics timeDate/timeSeries.
# Package: gmm
# Version: 1.0-4
# Date: 2009-03-10
# Title: Generalized Method of Moments and Generalized Empirical Likelihood
# Author: Pierre Chausse <pierre.chausse@uqam.ca>
# Maintainer: Pierre Chausse <pierre.chausse@uqam.ca>
# Description: It is a complete suite to estimate models based on moment
# conditions. It includes the two step Generalized method of moments
# (GMM) of Hansen(1982), the iterated GMM and continuous updated
# estimator (CUE) of Hansen-Eaton-Yaron(1996) and several methods that
# belong to the Generalized Empirical Likelihood (GEL) family of estimators,
# as presented by Smith(1997), Kitamura(1997), Newey-Smith(2004) and
# Anatolyev(2005).
# Depends: R (>= 2.0.0), sandwich, tseries, mvtnorm
# Imports: stats
# License: GPL (>= 2)
# ------------------------------------------------------------------------------
.gmm <-
function(g, x, t0=NULL, gradv=NULL, type=c("twoStep","cue","iterative"),
wmatrix = c("optimal","ident"), vcov=c("HAC","iid"),
kernel=c("Quadratic Spectral","Truncated", "Bartlett", "Parzen",
"Tukey-Hanning"),crit=10e-7,bw = .bwAndrews2,
prewhite = FALSE, ar.method = "ols", approx="AR(1)",tol = 1e-7,
itermax=100,intercept=TRUE,optfct=c("optim","optimize"), ...)
{
type <- match.arg(type)
kernel <- match.arg(kernel)
vcov <- match.arg(vcov)
wmatrix <- match.arg(wmatrix)
optfct <- match.arg(optfct)
typeg=0
if (is(g,"formula"))
{
typeg=1
dat <- .get_dat(g,x,intercept=intercept)
x <- dat$x
g <- function(tet,x,ny=dat$ny,nh=dat$nh,k=dat$k)
{
tet <- matrix(tet,ncol=k)
if (intercept)
{
e <- x[,1:ny] - x[,(ny+1):(ny+k)]%*%t(tet)
gt <- e
for (i in 2:nh)
{
gt <- cbind(gt,e*x[,(ny+k+i)])
}
}
if (!intercept)
e <- x[,1:ny] - x[,(ny+1):(ny+k)]%*%t(tet)
gt <- e*x[,ny+k+1]
if (nh > 1)
{
for (i in 2:nh)
{
gt <- cbind(gt,e*x[,(ny+k+i)])
}
}
return(gt)
}
gradv <- function(x,ny=dat$ny,nh=dat$nh,k=dat$k)
{
dgb <- -(t(x[,(ny+k+1):(ny+k+nh)])%*%x[,(ny+1):(ny+k)])%x%
diag(rep(1,ny))/nrow(x)
return(dgb)
}
tetlin <- function(x,w,ny=dat$ny,nh=dat$nh,k=dat$k)
{
n <- nrow(x)
ym <- as.matrix(x[,1:ny])
xm <- as.matrix(x[,(ny+1):(ny+k)])
hm <- as.matrix(x[,(ny+k+1):(ny+k+nh)])
whx <- solve(w,(crossprod(hm,xm)%x%diag(ny)))
wvecyh <- solve(w,matrix(crossprod(ym,hm),ncol=1))
dg <- gradv(x)
xx <- crossprod(dg,whx)
par <- solve(xx,crossprod(dg,wvecyh))
gb <- matrix(colSums(g(par,x))/n,ncol=1)
value <- crossprod(gb,solve(w,gb))
res <- list(par=par,value=value)
return(res)
}
}
if (optfct == "optimize")
{
n = nrow(g(t0[1],x))
q = ncol(g(t0[1],x))
k = 1
k2 <- k
df <- q-k
}
else
{
if (typeg)
{
k <- dat$k
k2 <- k*dat$ny
n <- nrow(x)
q <- dat$ny*dat$nh
df <- q-k*dat$ny
}
else
{
n = nrow(g(t0,x))
q = ncol(g(t0,x))
k = length(t0)
k2 <- k
df <- q-k
}
}
obj1 <- function(thet)
{
gt <- g(thet,x)
gbar <- as.vector(colMeans(gt))
obj <- crossprod(gbar,solve(w,gbar))
return(obj)
}
iid <- function(thet)
{
gt <- g(thet,x)
v <- crossprod(gt,gt)/n
return(v)
}
Gf <- function(thet)
{
myenv <- new.env()
assign('x',x,envir=myenv)
assign('thet',thet,envir=myenv)
barg <- function(x,thet)
{
gt <- g(thet,x)
gbar <- as.vector(colMeans(gt))
return(gbar)
}
G <- attr(numericDeriv(quote(barg(x,thet)),"thet",myenv),"gradient")
return(G)
}
if (q == k2 | wmatrix == "ident")
{
if (typeg)
{
w <- diag(q)
res <- tetlin(x,w)
z = list(par=res$par,objective=res$value)
}
else
{
w=diag(rep(1,q))
if (optfct == "optim")
res <- optim(t0,obj1, ...)
else
{
res <- optimize(obj1,t0, ...)
res$par <- res$minimum
res$value <- res$objective
}
z = list(par=res$par,objective=res$value)
}
}
else
{
if (type=="twoStep")
{
w=diag(rep(1,q))
if (typeg)
{
res1 <- tetlin(x,w)
}
else
{
if (optfct == "optim")
res1 <- optim(t0,obj1, ...)
else
{
res1 <- optimize(obj1,t0, ...)
res1$par <- res1$minimum
res1$value <- res1$objective
}
}
if (vcov == "iid")
w <- iid(res1$par)
if (vcov == "HAC")
w <- .HAC(g(res1$par,x), kernel=kernel, bw=bw,
prewhite=prewhite,ar.method=ar.method,approx=approx,tol=tol)
if (typeg)
{
res2 <- tetlin(x,w)
}
else
{
if (optfct == "optim")
res2 <- optim(res1$par,obj1, ...)
else
{
res2 <- optimize(obj1,t0, ...)
res2$par <- res2$minimum
res2$value <- res2$objective
}
}
z = list(par=res2$par,objective=res2$value)
}
if (type=="cue")
{
obj_cue <- function(thet)
{
gt <- g(thet,x)
gbar <- as.vector(colMeans(gt))
if (vcov == "iid")
w2 <- iid(thet)
if (vcov == "HAC")
w2 <- .HAC(g(thet,x), kernel=kernel, bw=bw,
prewhite=prewhite,ar.method=ar.method,approx=approx,tol=tol)
obj <- crossprod(gbar,solve(w2,gbar))
return(obj)
}
if (typeg)
{
if (is.null(t0))
t0 <- tetlin(x,diag(rep(1,q)))$par
if (optfct == "optim")
{
res2 <- optim(t0,obj_cue, ...)
}
else
{
res2 <- optimize(obj_cue,t0, ...)
res2$par <- res2$minimum
res2$value <- res2$objective
}
}
else
{
if (optfct == "optim")
res2 <- optim(t0,obj_cue, ...)
else
{
res2 <- optimize(obj_cue,t0, ...)
res2$par <- res2$minimum
res2$value <- res2$objective
}
}
z = list(par=res2$par,objective=res2$value)
}
if (type=="iterative")
{
w=diag(rep(1,q))
if (typeg)
res <- tetlin(x,w)
else
{
if (optfct == "optim")
res <- optim(t0,obj1, ...)
else
{
res <- optimize(obj1,t0, ...)
res$par <- res$minimum
res$value <- res$objective
}
}
ch <- 100000
j <- 1
while(ch>crit)
{
tet <- res$par
if (vcov == "iid")
w2 <- iid(tet)
if (vcov == "HAC")
w2 <- .HAC(g(tet,x), kernel=kernel, bw=bw,
prewhite=prewhite,ar.method=ar.method,approx=approx,tol=tol)
if (typeg)
res <- tetlin(x,w2)
else
{
if (optfct == "optim")
res <- optim(tet,obj1, ...)
else
{
res <- optimize(obj1,t0, ...)
res$par <- res$minimum
res$value <- res$objective
}
}
ch <- crossprod(abs(tet-res$par)/tet,abs(tet-res$par)/tet)
if (j>itermax)
{
cat("No convergence after ",itermax," iterations")
ch <- crit
}
j <- j+1
}
z = list(par=res$par,objective=res$value)
}
}
if (!is.function(gradv))
G <- Gf(z$par)
else
if (typeg)
G <- gradv(x)
else
G <- gradv(z$par,x)
if (vcov == "iid")
v <- iid(z$par)/n
else
v <- .HAC(g(z$par,x), kernel=kernel, bw=bw,prewhite=prewhite,
ar.method=ar.method,approx=approx,tol=tol)/n
if (wmatrix == "optimal")
{
z$vcov <- solve(crossprod(G,solve(v,G)))
}
else
{
GGG <- solve(crossprod(G),t(G))
z$vcov <- GGG%*%v%*%t(GGG)
}
z$gt <- g(z$par,x)
if (typeg==0)
names(z$par) <- paste("Theta[",1:k,"]",sep="")
if (typeg == 1)
{
namex <- colnames(dat$x[,(dat$ny+1):(dat$ny+dat$k)])
nameh <- colnames(dat$x[,(dat$ny+dat$k+1):(dat$ny+dat$k+dat$nh)])
if (dat$ny > 1)
{
namey <- colnames(dat$x[,1:dat$ny])
names(z$par) <- paste(rep(namey,dat$k),"_",rep(namex,rep(dat$ny,dat$k)),sep="")
colnames(z$gt) <- paste(rep(namey,dat$nh),"_",rep(nameh,rep(dat$ny,dat$nh)),sep="")
}
if (dat$ny == 1)
{
names(z$par) <- namex
colnames(z$gt) <- nameh
}
}
dimnames(z$vcov) <- list(names(z$par),names(z$par))
z$df <- df
z$k <- k
z$n <- n
z$met <- type
z$kernel <- kernel
class(z) <- "gmm"
z
}
# ------------------------------------------------------------------------------
.HAC <-
function(x, weights = .weightsAndrews2, bw = .bwAndrews2,
prewhite = FALSE, ar.method = "ols", kernel=c("Quadratic Spectral",
"Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), approx="AR(1)",
tol = 1e-7)
{
n.orig <- n <- nrow(x)
k <- ncol(x)
kernel=match.arg(kernel)
if(prewhite > 0)
{
var.fit <- ar(x, order.max = prewhite, demean = FALSE, aic = FALSE,
method = ar.method)
if(k > 1) D <- solve(diag(ncol(x)) - apply(var.fit$ar, 2:3, sum))
else D <- as.matrix(1/(1 - sum(var.fit$ar)))
x <- as.matrix(na.omit(var.fit$resid))
n <- n - prewhite
}
weights <- weights(x, ar.method = ar.method,kernel=kernel,bw=bw,
approx = approx, prewhite = 1, tol = tol)
if (length(weights) > n)
{
warning("more weights than observations, only first n used")
weights <- weights[1:n]
}
utu <- 0.5 * crossprod(x) * weights[1]
wsum <- n * weights[1]/2
w2sum <- n * weights[1]^2/2
if (length(weights) > 1) {
for (ii in 2:length(weights)) {
utu <- utu + weights[ii] * crossprod(x[1:(n -
ii + 1), , drop = FALSE], x[ii:n, , drop = FALSE])
wsum <- wsum + (n - ii + 1) * weights[ii]
w2sum <- w2sum + (n - ii + 1) * weights[ii]^2
}
}
utu <- utu + t(utu)
if(prewhite > 0) {
utu <- crossprod(t(D), utu) %*% t(D)
}
wsum <- 2 * wsum
w2sum <- 2 * w2sum
bc <- n^2/(n^2 - wsum)
df <- n^2/w2sum
rval <- utu/n.orig
return(rval)
}
# ------------------------------------------------------------------------------
.weightsAndrews2 <-
function(x, bw = .bwAndrews2, kernel = c("Quadratic Spectral",
"Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), approx = c("AR(1)",
"ARMA(1,1)"), prewhite = 1, ar.method = "ols", tol = 1e-7, verbose = FALSE)
{
kernel <- match.arg(kernel)
approx=match.arg(approx)
if (is.function(bw))
bw <- bw(x, kernel = kernel, prewhite = prewhite,
ar.method = ar.method, approx=approx)
n <- NROW(x)
weights <- .kweights(0:(n - 1)/bw, kernel = kernel)
weights <- weights[1:max(which(abs(weights) > tol))]
return(weights)
}
# ------------------------------------------------------------------------------
.bwAndrews2 <-
function(x, kernel = c("Quadratic Spectral",
"Truncated", "Bartlett", "Parzen", "Tukey-Hanning"), approx = c("AR(1)",
"ARMA(1,1)"), prewhite = 1, ar.method = "ols")
{
kernel <- match.arg(kernel)
approx <- match.arg(approx)
n <- nrow(x)
k <- ncol(x)
if (approx == "AR(1)") {
fitAR1 <- function(x) {
rval <- ar(x, order.max = 1, aic = FALSE, method = "ols")
rval <- c(rval$ar, sqrt(rval$var.pred))
names(rval) <- c("rho", "sigma")
return(rval)
}
ar.coef <- apply(x, 2, fitAR1)
denum <- sum((ar.coef["sigma", ]/(1 - ar.coef["rho",
]))^4)
alpha2 <- sum(4 * ar.coef["rho", ]^2 * ar.coef["sigma",
]^4/(1 - ar.coef["rho", ])^8)/denum
alpha1 <- sum(4 * ar.coef["rho", ]^2 * ar.coef["sigma",
]^4/((1 - ar.coef["rho", ])^6 * (1 + ar.coef["rho",
])^2))/denum
}
else {
fitARMA11 <- function(x) {
rval <- arima(x, order = c(1, 0, 1), include.mean = FALSE)
rval <- c(rval$coef, sqrt(rval$sigma2))
names(rval) <- c("rho", "psi", "sigma")
return(rval)
}
arma.coef <- apply(x, 2, fitARMA11)
denum <- sum(((1 + arma.coef["psi", ]) * arma.coef["sigma",
]/(1 - arma.coef["rho", ]))^4)
alpha2 <- sum(4 * ((1 + arma.coef["rho", ] *
arma.coef["psi", ]) * (arma.coef["rho", ] + arma.coef["psi",
]))^2 * arma.coef["sigma", ]^4/(1 - arma.coef["rho",
])^8)/denum
alpha1 <- sum(4 * ((1 + arma.coef["rho", ] *
arma.coef["psi", ]) * (arma.coef["rho", ] + arma.coef["psi",
]))^2 * arma.coef["sigma", ]^4/((1 - arma.coef["rho",
])^6 * (1 + arma.coef["rho", ])^2))/denum
}
rval <- switch(kernel, Truncated = {
0.6611 * (n * alpha2)^(1/5)
}, Bartlett = {
1.1447 * (n * alpha1)^(1/3)
}, Parzen = {
2.6614 * (n * alpha2)^(1/5)
}, "Tukey-Hanning" = {
1.7462 * (n * alpha2)^(1/5)
}, "Quadratic Spectral" = {
1.3221 * (n * alpha2)^(1/5)
})
return(rval)
}
# ------------------------------------------------------------------------------
.summary.gmm <-
function(object, interval=FALSE, ...)
{
z <- object
se <- sqrt(diag(z$vcov))
par <- z$par
tval <- par/se
j <- z$objective*z$n
ans <- list(met=z$met,kernel=z$kernel,algo=z$algo)
names(ans$met) <- "GMM method"
names(ans$kernel) <- "kernel for cov matrix"
ans$par <- round(cbind(par,se, tval, 2 * pnorm(abs(tval), lower.tail = FALSE)),5)
dimnames(ans$par) <- list(names(z$par),
c("Estimate", "Std. Error", "t value", "Pr(>|t|)"))
ans$J_test <- noquote(paste("Test-J degrees of freedom is ",z$df,sep=""))
ans$j <- noquote(cbind(j,ifelse(z$df>0,pchisq(j,z$df,lower.tail = FALSE),"*******")))
dimnames(ans$j) <- list("Test E(g)=0: ",c("J-test","Pz(>j)"))
if (interval != FALSE)
{
zs <- qnorm((1-interval)/2,lower.tail=FALSE)
ch <- zs*se
ans$interval <- cbind(par-ch,par+ch)
dimnames(ans$interval) <- list(names(par),c("Theta_lower","Theta_upper"))
}
class(ans) <- "summary.gmm"
ans
}
# ------------------------------------------------------------------------------
.lintest <-
function(object,R,c)
{
z <- object
dl <- nrow(R)
rest <- R%*%z$par - c
vcov_par <- if (inherits(z, "gmm")) z$vcov else z$vcov_par
vcov <- R%*%vcov_par%*%t(R)
h0 <- matrix(rep(NA,nrow(R)),ncol=1)
for (i in 1:nrow(R))
{
testnames <- names(z$par)[R[i,]!=0]
rn <- R[i,][R[i,]!=0]
if (rn[1] != 1)
h0[i] <- paste(rn[1],"*",testnames[1],sep="")
else
h0[i] <- testnames[1]
if (length(rn) > 1)
{
for (j in 2:length(rn))
{
if (rn[j] >= 0)
{
if (rn[j] != 1)
h0[i] <- paste(h0[i]," + ",rn[j],"*",testnames[j],sep="")
else
h0[i] <- paste(h0[i]," + ",testnames[j],sep="")
}
else
{
if (abs(rn[j]) != 1)
h0[i] <- paste(h0[i]," - ",abs(rn[j]),"*",testnames[j],sep="")
else
h0[i] <- paste(h0[i]," - ",testnames[j],sep="")
}
}
}
h0[i] <- paste(h0[i]," = ",c[i],sep="")
}
rh <- solve(vcov,rest)
ans <- list(description <- "Wald test for H0: R(Theta)=c")
ans$H0 <- noquote(h0)
colnames(ans$H0) <- "Null Hypothesis"
wt <- crossprod(rest,rh)
pv <- pchisq(wt,dl,lower.tail=FALSE)
res <- cbind(wt,pv)
dimnames(res) <- list("Wald test", c("Statistics","P-Value"))
ans$result <- res
ans
}
################################################################################
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