Dynamic Principal Components in the Time Domain

TL;DR

This paper introduces a flexible time domain method for defining dynamic principal components that can handle non-stationary data and outliers, extending previous stationary-based approaches.

Contribution

It presents a new time domain approach for dynamic principal components applicable to non-stationary and short series, including a robust version for outlier contamination.

Findings

Applicable to non-stationary and short series

Includes a robust method for outlier handling

Demonstrated with real datasets

Abstract

We propose a time domain approach to define dynamic principal components (DPC) using a reconstruction of the original series criterion. This approach to define DPC was introduced by Brillinger, who gave a very elegant theoretical solution in the stationary case using the cross spectrum. Our procedure can be applied under more general conditions including the case ofnon stationary series and relatively short series. We also present a robust version of our procedure that allows to estimate the DPC when the series have outlier contamination. Our non robust and robust procedures are illustrated with real datasets.