Frequency Domain Based Analysis: Dynamic PCA
Estimate cross-covariances of two stationary multivariate time series
Frequency-wise difference of freqdom objects
Time-wise difference of freqdom objects
Compute DPCA filter coefficients
Dynamic KL expansion
Compute Dynamic Principal Components and dynamic Karhunen Loeve extepa...
Obtain dynamic principal components scores
Proportion of variance explained
Convolute (filter) a multivariate time series using a time-domain filt...
Coefficients of a discrete Fourier transform
Computes the Fourier transformation of a filter given as timedom obj...
Frequency domain basde analysis: dynamic PCA
Eigendecompose a frequency domain operator at each frequency
Compute a matrix product of two frequency-domain operators
Create an object corresponding to a frequency domain functional
Compute a transpose of a given frequency-domain operator at each frequ...
Frequency-wise product of freqdom objects
Checks if an object belongs to the class freqdom
Checks if an object belongs to the class timedom
Frequency-wise sum of freqdom objects
Time-wise sum of freqdom objects
Frequency-wise sum of freqdom objects
Print freqdom object
Print timedom object
Simulate a multivariate autoregressive time series
Invert order of lags or grid parameters of a timedom or freqdom ob...
rev Reverts order of lags in an object of class timedom
Moving average process
Compute empirical spectral density
Print object summary
Print object summary
Compute operator norms of elements of a filter
Defines a linear filter
Choose lags of an object of class timedom
Implementation of dynamic principal component analysis (DPCA), simulation of VAR and VMA processes and frequency domain tools. These frequency domain methods for dimensionality reduction of multivariate time series were introduced by David Brillinger in his book Time Series (1974). We follow implementation guidelines as described in Hormann, Kidzinski and Hallin (2016), Dynamic Functional Principal Component <doi:10.1111/rssb.12076>.