# Spec_compare_localize_freq: Compare the spectral density operator of two Functional Time... In ftsspec: Spectral Density Estimation and Comparison for Functional Time Series

## Description

Compare the spectral density operator of two Functional Time Series and localize frequencies at which they differ.

## Usage

 1 2 3 Spec_compare_localize_freq(X, Y, B.T = (dim(X)[1])^(-1/5), W, autok = 2, subgrid.density, verbose = 0, demean = FALSE, K.fixed = NA, subgrid.density.relative.to.bandwidth) 

## Arguments

 X,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 autok A variable used to specify if (and which) pseudo-AIC criterion is used to select the truncation parameter K. subgrid.density Only used if subgrid=TRUE. Specifies the approximate number of frequencies within the bandwidth over which the periodogram operator is smoothed. 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. K.fixed The value of K used if autok=0. subgrid.density.relative.to.bandwidth logical parameter to specify if subgrid.density is specified relative to the bandwidth parameter B.T

## Details

X,Y must be of equal size T.len \times d, where T.len is the length of the time series, and d is the number of basis functions. Each row corresponds to a time point, and each column corresponds to the coefficient of the corresponding basis function of the FTS.

autok=0 returns the p-values for K=1, …, \code{K.fixed}. autok=1 uses the AIC criterion of Tavakoli \& Panaretos (2015), which is a generalization of the pseudo-AIC introduced in Panaretos et al (2010). autok=2 uses the AIC* criterion of Tavakoli \& Panaretos (2015), which is an extension of the AIC criterion that takes into account the difficulty associated with the estimation of eigenvalues of a compact operator.

## 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.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ma.scale2=ma.scale1=c(-1.4,2.3,-2) ma.scale2[3] = ma.scale1[3]+.0 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') ans0=Spec_compare_localize_freq(X, Y, W=Epanechnikov_kernel, autok=2, subgrid.density=10, verbose=0, demean=FALSE, subgrid.density.relative.to.bandwidth=TRUE) plot(ans0) plot(ans0, method='fdr') PvalAdjust(ans0, method='fdr') ## print FDR adjusted p-values abline(h=.05, lty=3) ans0=Spec_compare_localize_freq(X, Y, W=Epanechnikov_kernel, autok=0, subgrid.density=10, verbose=0, demean=FALSE, subgrid.density.relative.to.bandwidth=TRUE, K.fixed=4) ## fixed values of K plot(ans0) plot(ans0, 'fdr') plot(ans0, 'holm') PvalAdjust(ans0, method='fdr') rm(ans0) 

ftsspec documentation built on May 29, 2017, 9:36 a.m.