Spec_compare_fixed_freq {ftsspec}

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)