function: ARFIMA Forecasting

Description

Method for forecasting from an ARFIMA model.

Usage

arfimaforecast(fitORspec, data = NULL, n.ahead = 10, n.roll = 0, out.sample = 0, 
external.forecasts = list(mregfor = NULL), ...)

Arguments

Details

The forecast function has two dispatch methods allowing the user to call it with either a fitted object (in which case the data argument is ignored), or a specification object (in which case the data is required) with the parameters entered via the set.fixed<- methods on an ARFIMAspec object.
One step ahead forecasts are based on the value of the previous data, while n-step ahead (n>1) are based on the unconditional mean of the model.
The ability to roll the forecast 1 step at a time is implemented with the n.roll argument which controls how many times to roll the n.ahead forecast. The default argument of n.roll = 0 denotes no rolling beyond the first forecast and returns the standard n.ahead forecast. Critically, since n.roll depends on data being available from which to base the rolling forecast, the arfimafit function needs to be called with the argument out.sample being at least as large as the n.roll argument, or in the case of a specification being used instead of a fit object, the out.sample argument directly in the forecast function.

Value

A ARFIMAforecast object containing details of the ARFIMA forecast. See the class for details on the returned object and methods for accessing it and performing some tests.

Author(s)

Alexios Ghalanos

Examples

## Not run: 
# Long Horizon Forecast
data(sp500ret)	
fit = vector(mode = "list", length = 9)
dist = c("norm", "snorm", "std", "sstd", "ged", "sged", "nig", "ghyp", "jsu")
for(i in 1:9){
	spec = arfimaspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE, 
	arfima = FALSE), distribution.model = dist[i])
	fit[[i]] = arfimafit(spec = spec, data = sp500ret, solver = "solnp", 
	fit.control = list(scale = 1))
}
cfmatrix = matrix(NA, nrow = 9, ncol = 7)
colnames(cfmatrix) = c("mu", "ar1", "ma1", "sigma", "skew", "shape", "ghlambda")
rownames(cfmatrix) = dist

for(i in 1:9){
	cf = coef(fit[[i]])
	cfmatrix[i, match(names(cf), colnames(cfmatrix))] =  cf
}

umean = rep(0, 9)
for(i in 1:9){
	umean[i] = uncmean(fit[[i]])
}

forc = vector(mode = "list", length = 9)
for(i in 1:9){
	forc[[i]] = arfimaforecast(fit[[i]], n.ahead = 100)
}

lmean40 = sapply(forc, FUN = function(x) as.numeric(as.data.frame(x)[40,1]))
cfmatrix1 = cbind(cfmatrix, umean, lmean40)
colnames(cfmatrix1) = c(colnames(cfmatrix1[,1:7]), "uncmean", "forecast40")

# forecast with spec to check results
forc2 = vector(mode = "list", length = 9)
for(i in 1:9){
	spec = arfimaspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE, 
	arfima = FALSE), distribution.model = dist[i])
	setfixed(spec) = as.list(coef(fit[[i]]))
	forc2[[i]] = arfimaforecast(spec, data = sp500ret, n.ahead = 100)
}
lmean240 = sapply(forc2, FUN = function(x) as.numeric(as.data.frame(x)[40,1]))
cfmatrix2 = cbind(cfmatrix, umean, lmean240)
colnames(cfmatrix2) = c(colnames(cfmatrix2[,1:7]), "uncmean", "forecast40")

cat("\nARFIMAforecast from ARFIMAfit and ARFIMAspec check:")
cat("\nFit\n")	
print(cfmatrix1, digits = 4)
cat("\nSpec\n")	
print(cfmatrix2, digits = 4)
# methods and slots
slotNames(forc[[1]])
showMethods(classes="ARFIMAforecast")
# summary
show(forc[[1]])
# Extractor Functions
# as array (array dimension [3] is 1 since n.roll = 0 i.e. no rolling beyond 
# the first)
as.array(forc[[1]])
# as.data.frame
as.data.frame(forc[[1]])
# as.list
as.list(forc[[1]])

# Rolling Forecast
data(sp500ret)
fit = vector(mode = "list", length = 9)
dist = c("norm", "snorm", "std", "sstd", "ged", "sged", "nig", "ghyp", "jsu")
for(i in 1:9){
	spec = arfimaspec(mean.model = list(armaOrder = c(1,1), include.mean = TRUE, 
			arfima = FALSE), distribution.model = dist[i])
	fit[[i]] = arfimafit(spec = spec, data = sp500ret, solver = "solnp", 
			out.sample = 1000, fit.control = list(scale = 1))
}
cfmatrix = matrix(NA, nrow = 9, ncol = 7)
colnames(cfmatrix) = c("mu", "ar1", "ma1", "sigma", "skew", "shape", "ghlambda")
rownames(cfmatrix) = dist

for(i in 1:9){
	cf = coef(fit[[i]])
	cfmatrix[i, match(names(cf), colnames(cfmatrix))] =  cf
}


forc = vector(mode = "list", length = 9)
for(i in 1:9){
	forc[[i]] = arfimaforecast(fit[[i]], n.ahead = 1, n.roll = 999)
}
rollforc = sapply(forc, FUN = function(x) t(unlist(as.data.frame(x, 
	rollframe = "all", aligned = FALSE))))

# forecast performance measures:
fpmlist = vector(mode = "list", length = 9)
for(i in 1:9){
	fpmlist[[i]] = fpm(forc[[i]], summary = FALSE)
}

par(mfrow = c(1,2))
dd = rownames(tail(sp500ret, 1250))
clrs = rainbow(9, alpha = 1, start = 0.4, end = 0.95)
plot(as.Date(dd), tail(sp500ret[,1], 1250), type = "l", 
	ylim = c(-0.02, 0.02), col = "lightgrey", ylab = "", xlab = "", 
	main = "Rolling 1-ahead Forecasts\nvs Actual")
for(i in 1:9){
	tmp = tail(sp500ret[,1], 1250)
	tmp[251:1250] = rollforc[1:1000,i]
	lines(as.Date(dd), c(rep(NA, 250), tmp[-(1:250)]), col = clrs[i])
}
legend("topleft", legend = dist, col = clrs, fill = clrs, bty = "n")

# plot deviation measures and range
tmp = vector(mode = "list", length = 9)
for(i in 1:9){
	tmp[[i]] = fpmlist[[i]][,"AE"]
	names(tmp[[i]]) = dist[i]
}
boxplot(tmp, col = clrs, names = dist, range  = 6, notch = TRUE, 
		main = "Rolling 1-ahead Forecasts\nAbsolute Deviation Loss")

# fpm comparison
compm = matrix(NA, nrow = 3, ncol = 9)
compm = sapply(fpmlist, FUN = function(x) c(mean(x[,"SE"]), mean(x[,"AE"]), 
	mean(x[,"DAC"])))
colnames(compm) = dist
rownames(compm) = c("MSE", "MAD", "DAC")

cat("\nRolling Forecast FPM\n")
print(compm, digits = 4)
cat("\nMethods Check\n")
as.data.frame(forc[[1]], rollframe = 0)
as.data.frame(forc[[1]], rollframe = 999)
t(as.data.frame(forc[[1]], rollframe = "all", aligned = FALSE))
fpm(forc[[1]], summary = TRUE)
show(forc[[1]])

## End(Not run)