# Estimation of the Evolutionary Spectra with Application to Stationarity Test

arXiv: https://arxiv.org/abs/1802.09053 · HTML: https://mlsanity.com/paper/1802.09053/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2018.

## Built on by (most cited first, 4 of 4)

- [Learning Invariant Representations under General Interventions on the Response](https://mlsanity.com/paper/2208.10027/) (2022)
- [An Invariant Matching Property for Distribution Generalization under Intervened Response](https://mlsanity.com/paper/2205.09162/) (2022)
- [DynamicFL: Federated Learning with Dynamic Communication Resource Allocation](https://mlsanity.com/paper/2409.04986/) (2024)
- [Causal Inference from Slowly Varying Nonstationary Processes](https://mlsanity.com/paper/2405.06902/) (2024)

## Abstract (arXiv)

In this work, we propose a new inference procedure for understanding non-stationary processes, under the framework of evolutionary spectra developed by Priestley. Among various frameworks of modeling non-stationary processes, the distinguishing feature of the evolutionary spectra is its focus on the physical meaning of frequency. The classical estimate of the evolutionary spectral density is based on a double-window technique consisting of a short-time Fourier transform and a smoothing. However, smoothing is known to suffer from the so-called bias leakage problem. By incorporating Thomson's multitaper method that was originally designed for stationary processes, we propose an improved estimate of the evolutionary spectral density, and analyze its bias/variance/resolution tradeoff. As an application of the new estimate, we further propose a non-parametric rank-based stationarity test, and provide various experimental studies.