# Testing for stationarity of functional time series in the frequency domain

arXiv: https://arxiv.org/abs/1701.01741 · HTML: https://mlsanity.com/paper/1701.01741/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2017.

## Built on by (most cited first, 3 of 3)

- [Conformal Prediction Bands for Two-Dimensional Functional Time Series](https://mlsanity.com/paper/2207.13656/) (2022)
- [Bounds in Wasserstein Distance for Locally Stationary Functional Time Series](https://mlsanity.com/paper/2504.06453/) (2025)
- [Parametrising the Inhomogeneity Inducing Capacity of a Training Set, and its Impact on Supervised Learning](https://mlsanity.com/paper/2510.18332/) (2025)

## Abstract (arXiv)

Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new stationarity test for functional time series based on frequency domain methods. The proposed test statistics is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, explicitly allowing for frequency-dependent levels of truncation to adapt to the dynamics of the underlying functional time series. The properties of the test are derived both under the null hypothesis of stationary functional time series and under the smooth alternative of locally stationary functional time series. The methodology is theoretically justified through asymptotic results. Evidence from simulation studies and an application to annual temperature curves suggests that the test works well in finite samples.