Spec_compare_localize_freq_curvelength function

Compare the spectral density operator of two Functional Time Series and localize frequencies at which they differ, and (spatial) regions where they differ

Spec_compare_localize_freq_curvelength(X, Y, B.T = (dim(X)[1])^(-1/5), W,
  alpha = 0.05, accept = 0, reject = 1, verbose = 0, demean = FALSE)

Arguments

• X: The $T \times nbasis$ matrices of containing the coordinates, expressed in some functional basis, of the two FTS that to be compared. expressed in a basis.
• Y: The $T \times nbasis$ matrices of containing the coordinates, expressed in some functional basis, of the two FTS that to be compared. expressed in a basis.
• B.T: The bandwidth of frequencies over which the periodogram operator is smoothed. If B.T=0, the periodogram operator is returned.
• W: The weight function used to smooth the periodogram operator. Set by default to be the Epanechnikov kernel
• alpha: level for the test
• accept,reject: values for accepted, rejected regions
• verbose: A variable to show the progress of the computations. By default, verbose=0.
• demean: A logical variable to choose if the FTS is centered before computing its spectral density operator.

Examples

ma.scale2=ma.scale1=c(-1.4,2.3,-2)
ma.scale2[3] = ma.scale1[3]+.4
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=2^9, noise.type='wiener')
Y=Simulate_new_MA(a2, T.len=2^9, noise.type='wiener')
ans0=Spec_compare_localize_freq_curvelength(X, Y, W=Epanechnikov_kernel, alpha=.01, demean=TRUE)
print(ans0)
plot(ans0)
rm(ma.scale1, ma.scale2, a1, a2, X, Y, ans0)