Power spectral estimate for discrete data.

Area of Science:

• Time series analysis
• Signal processing
• Data science

Background:

• Identifying cycles in periodic signals is crucial for time series analysis.
• Real-world data often consists of discrete, non-equidistant events, frequently affected by noise and limited samples.
• Existing methods struggle with the spectral analysis of such discrete, noisy, and sparse datasets.

Purpose of the Study:

• To propose a novel method for power spectral estimation of discrete data.
• To explore the potential of edit distance for quantifying frequency content in discrete signals.
• To develop a robust tool for cycle detection in challenging real-world time series.

Main Methods:

• Defined a measure of serial dependence based on edit distance.
• Transformed this measure into a power spectral estimate (EDSPEC), analogous to the Wiener-Khinchin theorem.
• Applied EDSPEC to paradigmatic discrete signals (random, correlated, chaotic, periodic) and a novel catalog of European atmospheric rivers (ARs).

Main Results:

• EDSPEC effectively detects periodic cycles in discrete signals, outperforming traditional methods under noise and short data conditions.
• The method successfully identified seasonal and multi-annual cycles in European atmospheric rivers.
• Demonstrated the versatility of EDSPEC across various types of discrete event data.

Conclusions:

• The proposed EDSPEC method offers a powerful new approach for spectral analysis of discrete, non-equidistant time series data.
• EDSPEC is effective in identifying periodicities even in noisy and limited datasets, applicable to diverse scientific fields.
• This work opens new avenues for studying periodic discrete signals in complex systems, exemplified by the analysis of atmospheric rivers.