FEXPest: Fractional EXP (FEXP) Model Estimator

In longmemo: Statistics for Long-Memory Processes (Book Jan Beran), and Related Functionality

Fractional EXP (FEXP) Model Estimator

Description

FEXPest(x, *) computes Beran's Fractional EXP or ‘FEXP’ model estimator.

.ffreq(n) returns the Fourier frequencies \frac{2\pi j}{n} (of a time series of length n).

Usage

FEXPest(x, order.poly, pvalmax, verbose = FALSE)
## S3 method for class 'FEXP'
print(x, digits = getOption("digits"), ...)

.ffreq(n, full = FALSE)

Arguments

x	numeric vector representing a time series.
order.poly	integer specifying the maximal polynomial order that should be taken into account. order.poly = 0 is equivalent to a FARIMA(0,d,0) model.
pvalmax	maximal P-value – the other iteration stopping criterion and “model selection tuning parameter”. Setting this to 1, will use order.poly alone, and hence the final model order will be = order.poly.
verbose	logical indicating if iteration output should be printed.
digits, ...	optional arguments for print method, see print.default.
n	a positive integer, typically the length of a time series.
full	logical indicating if n %/% 2 or by default “only” (n-1) %/% 2 values should be returned.

Value

FEXPest(x,..) returns an object of class FEXP, basically a list with components

call	the function call.
n	time series length length(x).
H	the “Hurst” parameter which is simply (1-theta[2])/2.
coefficients	numeric 4-column matrix as returned from summary.glm(), with estimate of the full parameter vector \theta, its standard error estimates, t- and P-values, as from the glm(*, family = Gamma) fit.
order.poly	the effective polynomial order used.
max.order.poly	the original order.poly (argument).
early.stop	logical indicating if order.poly is less than max.order.poly, i.e., the highest order polynomial terms were dropped because of a non-significant P-value.
spec	the spectral estimate f(\omega_j), at the Fourier frequencies \omega_j. Note that .ffreq(x$n) recomputes the Fourier frequencies vector (from a fitted FEXP or WhittleEst model x).
yper	raw periodogram of (centered and scaled x) at Fourier frequencies I(\omega_j).

There currently are methods for print(), plot and lines (see plot.FEXP) for objects of class "FEXP".

Author(s)

Martin Maechler, using Beran's “main program” in Beran(1994), p.234 ff

References

Beran, Jan (1993) Fitting long-memory models by generalized linear regression. Biometrika 80, 817–822.

Beran, Jan (1994). Statistics for Long-Memory Processes; Chapman & Hall.

See Also

WhittleEst; the plot method, plot.FEXP.

Examples

data(videoVBR)
(fE  <- FEXPest(videoVBR, order = 3, pvalmax = .5))
(fE3 <- FEXPest(videoVBR, order = 3, pvalmax = 1 ))

(fE7 <- FEXPest(videoVBR, order = 3, pvalmax = 0.10))
##--> this also choses order 2, as "FE" :
all.equal(fE $coef,
          fE7$coef) # -> TRUE

confint(fE)
confint(fE7, level = 0.99)

.ffreq(8)
.ffreq(8, TRUE)
stopifnot(all.equal((1:3)/4,
                    .ffreq(8) / pi))

longmemo documentation built on Aug. 8, 2025, 6:15 p.m.