rugarch (version 1.0-3)

arfimafilter-methods: function: ARFIMA Filtering

Description

Method for filtering an ARFIMA model.

Usage

arfimafilter(spec, data, out.sample = 0, n.old=NULL, ...)

Arguments

data

A univariate data object. Can be a numeric vector, matrix, data.frame, zoo, xts, timeSeries, ts or irts object.

spec

An ARFIMA spec object of class ARFIMAspec with the fixed.pars argument having the model parameters on which the filtering is to take place.

out.sample

A positive integer indicating the number of periods before the last to keep for out of sample forecasting (as in arfimafit function).

n.old

For comparison with ARFIMA models using the out.sample argument, this is the length of the original dataset (see details).

...

.

Value

• A ARFIMAfilter object containing details of the ARFIMA filter.

Details

The n.old argument is optional and indicates the length of the original data (in cases when this represents a dataseries augmented by newer data). The reason for using this is so that the old and new datasets agree since the original recursion uses the sum of the residuals to start the recursion and therefore is influenced by new data. For a small augmentation the values converge after x periods, but it is sometimes preferable to have this option so that there is no forward looking information contaminating the study.

Examples

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
}
sk = ku = rep(0, 9)
for(i in 1:9){
	cf = coef(fit[[i]])
	if(fit[[i]]@model$modelinc[16]>0) sk[i] = dskewness(distribution = dist[i], 
				skew = cf["skew"], shape = cf["shape"], lambda = cf["ghlambda"])		
	if(fit[[i]]@model$modelinc[17]>0) ku[i] = dkurtosis(distribution = dist[i], 
				skew = cf["skew"], shape = cf["shape"], lambda = cf["ghlambda"])
}
hq = sapply(fit, FUN = function(x) infocriteria(x)[4])
cfmatrix = cbind(cfmatrix, sk, ku, hq)
colnames(cfmatrix)=c(colnames(cfmatrix[,1:7]), "skewness", "ex.kurtosis","HQIC")


# filter the data to check results
filt = 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]]))
	filt[[i]] = arfimafilter(spec = spec, data = sp500ret)
}
print(cfmatrix, digits = 4)
cat("\nARFIMAfit and ARFIMAfilter residuals check:\n")
print(head(sapply(filt, FUN = function(x) residuals(x))) == head(sapply(fit, 
FUN = function(x) residuals(x))))
cat("\nas.data.frame method:\n")
print(cbind(head(as.data.frame(filt[[1]])), head(as.data.frame(fit[[1]]))))
cat("\ncoef method:\n")
print(cbind(coef(filt[[1]]), coef(fit[[1]])))
cat("\nfitted method:\n")
print(cbind(head(fitted(filt[[1]])), head(fitted(fit[[1]]))))
cat("\ninfocriteria method:\n")
# For filter, it assumes estimation of parameters else does not make sense!
print(cbind(infocriteria(filt[[1]]), infocriteria(fit[[1]])))
cat("\nlikelihood method:\n")
print(cbind(likelihood(filt[[1]]), likelihood(fit[[1]])))
cat("\nresiduals method:\n")
# Note that we the package will always return the full length residuals and 
# fitted object irrespective of the lags (i.e. since this is an ARMA(1,1) 
# i.e. max lag = 1, the first row is zero and should be discarded.
print(cbind(head(residuals(filt[[1]])), head(residuals(fit[[1]]))))
cat("\nuncmean method:\n")
print(cbind(uncmean(filt[[1]]), uncmean(fit[[1]])))
cat("\nuncmean method (by simulation):\n")
# For spec and fit
spec = arfimaspec( mean.model = list(armaOrder = c(1,1), include.mean = TRUE, 
arfima = FALSE), distribution.model = dist[1])
setfixed(spec) = as.list(coef(fit[[1]]))
print(cbind(uncmean(spec, method = "simulation", n.sim = 100000, rseed = 100), 
uncmean(fit[[1]], method = "simulation", n.sim = 100000, rseed = 100)))
cat("\nsummary method:\n")
show(filt[[1]])
show(fit[[1]])