freqdom.fda-package {freqdom.fda}

Functional time series: dynamic FPCA

Description

Implementation of dynamic functional principle component analysis (FDPCA), simulation of functional AR and functional MA processes and frequency domain tools for funcional data. The package is a wrapper for functionality of the multivariate package freqdom for applying frequency domain on objects from fda. Compared to freqdom some new visualization methods are added – adequate only if data has functional structure.

Details

fda.ts package allows you to analyse functional time series objects in both time and frequency domain. The main feature is dynamic functional principal component analysis. This method allows to transform a stationary functional time series into a vector process with mutually uncorrelated component processes.

There are two key differnces between classical PCA and dynamic PCA:

• Component processes returned by the dynamic procedure are mutually uncorrelated,

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

For functional data one can conveniently visualize properties of the filters, covariances or the spectral density operator.

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

The package fda.ts require the package freqdom provides the analogue multivariate toolset.

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.