longmemo (version 1.1-3)

FEXPest: 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 FEXP
print(x, digits = getOption("digits"), ...)
.ffreq(n, full = FALSE)

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".

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.

Author

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))