Spec_compare_fixed_freq function

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

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)

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.

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)

References

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

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

See Also

Spec_compare_localize_freq