Transformation cost spectrum for irregularly sampled time series

TL;DR

This paper introduces a novel method for analyzing irregularly sampled time series by transforming them into a spectrum of regularly sampled, stationary series with minimal information loss, enabling better detection of regime transitions.

Contribution

It proposes a transformation cost spectrum approach that preserves data integrity and facilitates regime transition analysis in irregular time series, validated on climate data.

Findings

Effective identification of climate transition periods

Minimal data distortion compared to interpolation methods

Applicable to diverse irregular time series

Abstract

Irregularly sampled time series analysis is a common problem in various disciplines. Since conventional methods are not directly applicable to irregularly sampled time series, a common interpolation approach is used; however, this causes data distortion and consequently biases further analyses. We propose a method that yields a regularly sampled time series spectrum of costs with minimum information loss. Each time series in this spectrum is a stationary series and acts as a difference filter. The transformation costs approach derives the differences between consecutive and arbitrarily sized segments. After obtaining regular sampling, recurrence plot analysis is performed to distinguish regime transitions. The approach is applied to a prototypical model to validate its performance and to different palaeoclimate proxy data sets located around Africa to identify critical climate transition periods during the last 5 million years and their characteristic properties.