freqdom-package {freqdom}

Frequency domain basde analysis: dynamic PCA

Description

Implementation of dynamic principle component analysis (DPCA), simulation of VAR and VMA processes and frequency domain tools. The package also provides a toolset for developers simplifying construction of new frequency domain based methods for multivariate signals.

Details

freqdom package allows you to manipulate time series objects in both time and frequency domains. We implement dynamic principal component analysis methods, enabling spectral decomposition of a stationary vector time series into uncorrelated components.

Dynamic principal component analysis enables estimation of temporal filters which transform a vector time series into another vector time series with uncorrelated components, maximizing the long run variance explained. There are two key differnces between classical PCA and dynamic PCA:

• Components returned by the dynamic procedure are uncorrelated in time, i.e. for any i \neq j and l \in Z, Y_i(t) and Y_j(t_l) are uncorrelated,

• The mapping maximizes the long run variance, which, in case of stationary vector time series, means that the process reconstructed from and d > 0 first dynamic principal components better approximates your vector time series process than the first d classic principal components.

For details, please refer to literature below and to help pages of functions dpca for estimating the components, dpca.scores for estimating scores and dpca.KLexpansion for retrieving the signal from components.

Apart from frequency domain techniques for stationary vector time series, freqdom provides a toolset of operators such as the vector Fourier Transform (fourier.transform) or a vector spectral density operator (spectral.density) as well as simulation of vector time series models rar, rma generating vector autoregressive and moving average respectively. These functions enable developing new techniques based on the Frequency domain analysis.

References

Hormann Siegfried, Kidzinski Lukasz and Hallin Marc. Dynamic functional principal components. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 77.2 (2015): 319-348.

Hormann Siegfried, Kidzinski Lukasz and Kokoszka Piotr. Estimation in functional lagged regression. Journal of Time Series Analysis 36.4 (2015): 541-561.

Hormann Siegfried and Kidzinski Lukasz. A note on estimation in Hilbertian linear models. Scandinavian journal of statistics 42.1 (2015): 43-62.