FEXPest: Fractional EXP (FEXP) Model Estimator

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

Description

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

Usage

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

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.

Value

An object of class FEXP which is 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 θ, 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(ω_j), at the Fourier frequencies ω_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(ω_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)

Example output

'FEXP' estimator, call:  FEXPest(x = videoVBR, order.poly = 3, pvalmax = 0.5) 
 polynomial order 2 - selected by stopping early (P = 0.99452 > pvalmax); H = 0.8563269
 coefficients 'theta' =
                  Estimate   Std. Error   t value   Pr(>|t|)
(Intercept)     3.79851575   0.04397787  86.37335 < 2.22e-16
1 - 2*H        -0.71265388   0.14870250  -4.79248 2.1813e-06
poly(ffr, j)1 -33.86448708   2.61036735 -12.97307 < 2.22e-16
poly(ffr, j)2   8.17740292   1.64429012   4.97321 9.0962e-07
  ==>            H = 0.856  (0.074) 
 <==> d := H - 1/2 = 0.356  (0.074) 

 $ early.stop: logi TRUE
 $ maxPv     : num 0.995
 $ yper      : num [1:499] 5145 22812 40031 7476 33737 ...
 $ spec      : num [1:499] 51315 30682 22521 17979 15029 ...
'FEXP' estimator, call:  FEXPest(x = videoVBR, order.poly = 3, pvalmax = 1) 
 polynomial order 3 - user specified; H = 0.8568971
 coefficients 'theta' =
                  Estimate   Std. Error  t value   Pr(>|t|)
(Intercept)     3.79852281   0.04403231 86.26672 < 2.22e-16
1 - 2*H        -0.71379427   0.20851944 -3.42315 0.00067043
poly(ffr, j)1 -33.84546050   3.53106292 -9.58506 < 2.22e-16
poly(ffr, j)2   8.16767139   2.09431166  3.89993 0.00010953
poly(ffr, j)3   0.00946287   1.37726161  0.00687 0.99452072
  ==>            H = 0.857  (0.104) 
 <==> d := H - 1/2 = 0.357  (0.104) 

 $ early.stop: logi FALSE
 $ maxPv     : NULL
 $ yper      : num [1:499] 5145 22812 40031 7476 33737 ...
 $ spec      : num [1:499] 51430 30728 22545 17993 15038 ...
'FEXP' estimator, call:  FEXPest(x = videoVBR, order.poly = 3, pvalmax = 0.1) 
 polynomial order 2 - selected by stopping early (P = 0.99452 > pvalmax); H = 0.8563269
 coefficients 'theta' =
                  Estimate   Std. Error   t value   Pr(>|t|)
(Intercept)     3.79851575   0.04397787  86.37335 < 2.22e-16
1 - 2*H        -0.71265388   0.14870250  -4.79248 2.1813e-06
poly(ffr, j)1 -33.86448708   2.61036735 -12.97307 < 2.22e-16
poly(ffr, j)2   8.17740292   1.64429012   4.97321 9.0962e-07
  ==>            H = 0.856  (0.074) 
 <==> d := H - 1/2 = 0.356  (0.074) 

 $ early.stop: logi TRUE
 $ maxPv     : num 0.995
 $ yper      : num [1:499] 5145 22812 40031 7476 33737 ...
 $ spec      : num [1:499] 51315 30682 22521 17979 15029 ...
[1] TRUE
                   2.5 %     97.5 %
(Intercept)     3.712321   3.884711
1 - 2*H               NA         NA
poly(ffr, j)1 -38.980713 -28.748261
poly(ffr, j)2   4.954654  11.400152
                   0.5 %     99.5 %
(Intercept)     3.685236   3.911795
1 - 2*H               NA         NA
poly(ffr, j)1 -40.588348 -27.140626
poly(ffr, j)2   3.941992  12.412814

longmemo documentation built on March 26, 2020, 7:42 p.m.