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#
# Simulation experiments:
# the series in the data set 'llmseas' are fit by
# maximizing the spectral log-likelihood function (ML-FD)
# where one of the parameters is concentrated out of
# the likelihood function
#
# the following procedures are considered:
# procedure 0: StructTS(), benchmark results
# procedure 1: ML-FD Netwon-Raphson
# procedure 2: ML-FD scoring algorithm
# procedure 3: ML-FD BFGS algorithm from 'optim()'
# procedure 4: ML-FD L-BFGS-B algorithm from 'optim()'
#
library("stsm")
# load data
##NOTE
# requires data set generated in file "datagen-llmseas.R" in the
# same folder as this file
iter <- ncol(llmseas)
# initial parameter values
initpars <- c(var2 = 1, var3 = 1)
initcpar <- c(var1 = 1)
nop <- NULL
# scoring algorithm parameters
tol <- 0.001
maxiter <- 100 #250
step <- NULL # (ignored for 'maxlik.fd.optim()')
# line search parameters
# they are ignored if 'step' is fixed to a numeric, e.g. 'step <- 1'
ls <- list(type = "optimize", tol = .Machine$double.eps^0.25, cap = 1)
#ls <- list(type = "brent.fmin", tol = .Machine$double.eps^0.25, cap = 1)
#ls <- list(type = "wolfe", ftol = 0.0001, gtol = 0.5, cap = 1)
# parameterization
transP <- NULL #NULL #"StructTS" #"square"
# barrier term in log-likelihood function (no barrier with mu = 0)
bar <- list(type = "1", mu = 0)
# storage list
Mres <- vector("list", 6)
names(Mres) <- paste("proc", 0:(length(Mres) - 1), sep = "")
tmp1 <- array(dim = c(iter, length(initpars) + 1),
dimnames = list(NULL, names(c(initcpar, initpars))))
tmp2 <- rep(NA, iter)
tmp3 <- array(dim = c(maxiter + 1, length(initpars) + 1, iter))
tmp4 <- array(dim = c(iter, 2), dimnames = list(NULL, c("fcn", "grd")))
Mres <- lapply(Mres, function(x) list(M = tmp1, iter = tmp2,
time = tmp2, paths = tmp3, lscounts = tmp4))
rm(tmp1, tmp2, tmp3, tmp4)
# graphical parameters to trace the simulation
plotid <- c(1, 2, 4) + 1
#plab <- names(Mres)[plotid]
plab <- c("StructTS", "Newton-Raphson", "Scoring", "BFGS", "L-BFGS-B")[plotid]
colors <- c("red", "green", "blue")
arrow.angle <- c(20, 30, 40)
legtext <- NULL
# begin main loop
for (i in seq_len(iter))
{
m <- stsm.model(model = "llm+seas", y = llmseas[,i],
pars = initpars, cpar = initcpar, nopars = nop, transPars = transP)
# procedure 0: ML-TD StructTS(), benchmark results
res0 <- StructTS(m@y, type = "BSM",
fixed = c(NA, 0, NA, NA))$coef[c(4,1,3)]
Mres$proc0$M[i,] <- res0
#i=1
# epsilon level seas
#172.29956 35.51876 176.74453
# procedure 1: ML-FD Netwon-Raphson
# with optimized step length if 'step' is NULL
res1 <- maxclik.fd.scoring(m = m, step = NULL,
information = "observed", ls = ls, barrier = bar,
control = list(maxit = maxiter, tol = tol, trace = TRUE))
Mres$proc1$M[i,] <- c(res1$model@cpar, res1$model@cpar * res1$par)
Mres$proc1$iter[i] <- res1$iter
Mres$proc1$paths[seq(res1$iter+1),,i] <- res1$Mpars
if (length(res1$ls.counts) == 2) # 'optimize()' does not return this
Mres$proc1$lscounts[i,] <- res1$ls.counts
#i=1
#> res1$par
# var2 var3
#0.05535256 0.82006341
#> res1$iter
#[1] 8
#> get.cpar(res1$model, rescale = TRUE)
# var1
#200.3328
#> get.pars(res1$model, rescale = TRUE)
# var2 var3
# 11.08893 164.28562
#> c(res1$model@cpar, res1$model@cpar * res1$par)
# var1 var2 var3
#200.33282 11.08893 164.28562
#> coef(res1)
# var1 var2 var3
#200.33282 11.08893 164.28562
# procedure 2: ML-FD scoring algorithm
# with optimized step length if 'step' is NULL
res2 <- maxclik.fd.scoring(m = m, step = NULL,
information = "expected", ls = ls, barrier = bar,
control = list(maxit = maxiter, tol = tol, trace = TRUE))
Mres$proc2$M[i,] <- c(res2$model@cpar, res2$model@cpar * res2$par)
Mres$proc2$iter[i] <- res2$iter
Mres$proc2$paths[seq(res2$iter+1),,i] <- res2$Mpars
if (length(res2$ls.counts) == 2)
Mres$proc2$lscounts[i,] <- res2$ls.counts
#i=1
#> res2$par
# var2 var3
#0.05535222 0.82002091
#> res2$iter
#[1] 6
#> get.cpar(res2$model, rescale = TRUE)
# var1
#200.3375
#> get.pars(res2$model, rescale = TRUE)
# var2 var3
# 11.08912 164.28091
#> c(res2$model@cpar, res2$model@cpar * res2$par)
# var1 var2 var3
#200.33746 11.08912 164.28091
# procedure 3: ML-FD BFGS algorithm from 'optim()'
# NOTE 'count' is recorded (not 'iter')
res3 <- try(maxlik.fd.optim(m, inf = 99999, method = "BFGS",
gr = "analytical"), silent = TRUE)
#res3 <- try(maxlik.fd.optim(m, inf = 99999, method = "BFGS",
# gr = "numerical"), silent = TRUE)
if (!inherits(res3, "try-error"))
{
Mres$proc3$M[i,] <- c(res3$model@cpar, res3$model@cpar * res3$par)
Mres$proc3$iter[i] <- res3$iter[1]
}
#i=1
#> res3$par
# var2 var3
#0.05535264 0.82006470
#> res3$iter
#function gradient
# 52 13
#> get.cpar(res3$model, rescale = TRUE)
# var1
#200.3327
#> get.pars(res3$model, rescale = TRUE)
# var2 var3
# 11.08894 164.28574
#> c(res3$model@cpar, res3$model@cpar * res3$par)
# var1 var2 var3
#200.33265 11.08894 164.28574
# procedure 4: ML-FD L-BFGS-B algorithm from 'optim()'
#res4 <- try(maxlik.fd.optim(m, barrier = bar, inf = 99999,
# method = "L-BFGS-B", gr = "analytical"), silent = TRUE)
res4 <- try(maxlik.fd.optim(m, barrier = bar, inf = 99999,
method = "L-BFGS-B", gr = "numerical"), silent = TRUE)
# record the path followed by the optimization method
# using the same stopping criterion as in 'maxlik.fd.scoring()'
if (!inherits(res4, "try-error"))
{
Mpars <- c(get.cpar(m, TRUE), get.pars(m, TRUE))
conv <- FALSE
r <- 0
while (!conv)
{
optout <- maxlik.fd.optim(m = m, barrier = bar, inf = 99999,
#method = "L-BFGS-B", gr = "analytical", hessian = FALSE,
method = "L-BFGS-B", gr = "numerical",
optim.control = list(trace = FALSE, maxit = r))
#Mpars <- rbind(Mpars, optout$par)
Mpars <- rbind(Mpars,
c(get.cpar(optout$model, TRUE), get.pars(optout$model, TRUE)))
#conv <- optout$convergence == 0
if (sqrt(sum((Mpars[r+1,-1] - Mpars[r+2,-1])^2)) < tol || r > maxiter)
conv <- TRUE
r <- r + 1
}
Mres$proc4$M[i,] <- Mpars[r+1,]
Mres$proc4$iter[i] <- r
Mres$proc4$paths[seq(r+1),,i] <- Mpars
}
#i=1
#> res4$par
# var2 var3
#0.05538285 0.82012291
#> r
#[1] 13
#> get.cpar(res4$model, rescale = TRUE)
# var1
#200.315
#> get.pars(res4$model, rescale = TRUE)
# var2 var3
# 11.09402 164.28293
#> c(res4$model@cpar, res4$model@cpar * res4$par)
# var1 var2 var3
#200.31502 11.09402 164.28293
# trace simulation
# '[,-1,i]' the first column is removed,
# it is the value inferred from the maximized likelihood
# the parameter concentrated out of the likelihood function
tmp <- rbind(na.omit(Mres$proc1$paths[,-1,i]), na.omit(Mres$proc2$paths[,-1,i]),
na.omit(Mres$proc3$paths[,-1,i]), na.omit(Mres$proc4$paths[,-1,i]))
rg <- apply(tmp, 2, range)
options(warn = -1)
plot(rg[,1], rg[,2], type = "n", xlab = "var2", ylab = "var3",
main = paste("series", i))
for (k in seq_along(plotid))
{
idk <- plotid[k]
mp <- na.omit(Mres[[idk]]$paths[,,i])
if (length(mp) > 0)
{
for (j in seq(2, nrow(mp)))
{
arrows(mp[j-1,2], mp[j-1,3], mp[j,2], mp[j,3],
lty = 1, col = colors[k], length = 0.15, angle = arrow.angle[k])
}
}
legtext <- c(legtext,
paste(plab[k], ": ", Mres[[idk]]$iter[i], " iter.", sep = ""))
}
legend("topright", legtext, cex = 1, adj = 0,
col = colors, lty = 1, xjust = 0, yjust = 2.0, bty = "n", horiz = FALSE)
legtext <- NULL
options(warn = 0)
#print(i)
trace.iter <- 100 * (i / iter)
if (trace.iter %% 10 == 0)
{
cat(paste(trace.iter, "% complete.\n", sep = ""))
#print(colMeans(Mres$proc1$M, na.rm = TRUE))
#print(colMeans(Mres$proc2$M, na.rm = TRUE))
#print(colMeans(Mres$proc3$M, na.rm = TRUE))
#print(colMeans(Mres$proc4$M, na.rm = TRUE))
}
}
# store results
#setwd("")
#save(Mres, file = "sim-llmseas-mcl-fd.rda")
# summary of results
colMeans(Mres$proc0$M)
colMeans(Mres$proc1$M)
colMeans(Mres$proc2$M)
colMeans(Mres$proc3$M)
colMeans(Mres$proc4$M)
> colMeans(Mres$proc2$M)
var1 var2 var3
291.40347 11.22479 107.83065
> colMeans(Mres$proc4$M)
var1 var2 var3
290.79962 11.22067 108.38712
summary(Mres$proc1$M)
mean(Mres$proc0$iter)
mean(Mres$proc1$iter)
mean(Mres$proc2$iter)
mean(Mres$proc3$iter)
mean(Mres$proc4$iter)
> mean(Mres$proc2$iter)
[1] 4.56
> mean(Mres$proc4$iter)
[1] 11.832
summary(Mres$proc2$iter)
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