FEXPest: Fractional EXP (FEXP) Model Estimator

Description

Computes Beran's Fractional EXP or ‘FEXP’ model estimator.

Usage

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

Arguments

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.

Value

An object of class FEXP which is basically a list with components

call

the function call.

time series length length(x).

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".

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.

Examples

Run this code

# NOT RUN {
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)
# }