How Many Components should be Retained from a Multivariate Time Series PCA?

TL;DR

This paper introduces two innovative methods, heat maps and angle analysis, to determine the optimal number of principal components to retain in multivariate time series analysis, enhancing understanding of their structure and evolution.

Contribution

It presents two novel approaches—heat map visualization and angle change analysis—for assessing principal component retention in multivariate time series.

Findings

Heat maps reveal component structure evolution over time.

Angle analysis provides insights into component stability.

Both methods improve understanding of multivariate time series structure.

Abstract

We report on the results of two new approaches to considering how many principal components to retain from an analysis of a multivariate time series. The first is by using a "heat map" based approach. A heat map in this context refers to a series of principal component coefficients created by applying a sliding window to a multivariate time series. Furthermore the heat maps can provide detailed insights into the evolution of the structure of each principal component over time. The second is by examining the change of the angle of the principal component over time within the high-dimensional data space. We provide evidence that both are useful in studying structure and evolution of a multivariate time series.