Spec_compare_fixed_freq: Test if two spectral density operators at some fixed...

In ftsspec: Spectral Density Estimation and Comparison for Functional Time Series

Test if two spectral density operators at some fixed frequency are equal.

Description

A test for the null hypothesis that two spectral density operators (at the same frequency \omega) are equal, using a pseudo-AIC criterion for the choice of the truncation parameter. (used in Spec_compare_localize_freq)

Usage

Spec_compare_fixed_freq(
  spec1,
  spec2,
  is.pi.multiple,
  m,
  kappa.square,
  autok = 2,
  K.fixed = NA
)

Arguments

spec1, spec2	The two sample spectral densities (at the same frequency \omega) to be compared.
is.pi.multiple	A logical variable, to specify if \omega = {0, \pi} or not.
m	The number of Fourier frequencies over which the periodogram operator was smoothed.
kappa.square	the L2-norm of the weight function used to estimate the spectral density operator
autok	A variable used to specify if (and which) pseudo-AIC criterion is used to select the truncation parameter K.
K.fixed	The value of K used if autok=0.

References

Tavakoli, Shahin and Panaretos, Victor M. "Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics", 2014, under revision

Panaretos, Victor M., David Kraus, and John H. Maddocks. "Second-order comparison of Gaussian random functions and the geometry of DNA minicircles." Journal of the American Statistical Association 105.490 (2010): 670-682.

See Also

Spec_compare_localize_freq

Examples

ma.scale2=ma.scale1=c(-1.4,2.3,-2)
ma.scale2[3] = ma.scale1[3]+.3
a1=Generate_filterMA(10, 10, MA.len=3, ma.scale=ma.scale1)
a2=Generate_filterMA(10, 10, MA.len=3, ma.scale=ma.scale2)
X=Simulate_new_MA(a1, T.len=512, noise.type='wiener')
Y=Simulate_new_MA(a2, T.len=512, noise.type='wiener') 
spec.X = Spec(X)
spec.Y = Spec(Y)
Spec_compare_fixed_freq(spec.X$spec[1,,], spec.Y$spec[1,,],
is.pi.multiple=TRUE, spec.X$m, spec.X$kappa.square)

ftsspec documentation built on Aug. 4, 2026, 9:07 a.m.