# AZ-whiteness test: a test for uncorrelated noise on spatio-temporal graphs

arXiv: https://arxiv.org/abs/2204.11135 · HTML: https://mlsanity.com/paper/2204.11135/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 24 references that are in the map.
- First posted on arXiv 23 Apr 2022.

## Builds on (most cited first, 4 of 4)

- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Filling the G_ap_s: Multivariate Time Series Imputation by Graph Neural Networks](https://mlsanity.com/paper/2108.00298/) (2021)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [Multivariate Time Series Forecasting with Latent Graph Inference](https://mlsanity.com/paper/2203.03423/) (2022)

## Built on by (most cited first, 5 of 5)

- [Graph Neural Networks for temporal graphs: State of the art, open challenges, and opportunities](https://mlsanity.com/paper/2302.01018/) (2023)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Sparse Graph Learning from Spatiotemporal Time Series](https://mlsanity.com/paper/2205.13492/) (2022)
- [Contextualizing MLP-Mixers Spatiotemporally for Urban Data Forecast at Scale](https://mlsanity.com/paper/2307.01482/) (2023)
- [ChaosNetBench: Benchmarking Spatio-Temporal Graph Neural Networks on Chaotic Lattice Dynamics](https://mlsanity.com/paper/2605.09676/) (2026)

## Abstract (arXiv)

We present the first whiteness test for graphs, i.e., a whiteness test for multivariate time series associated with the nodes of a dynamic graph. The statistical test aims at finding serial dependencies among close-in-time observations, as well as spatial dependencies among neighboring observations given the underlying graph. The proposed test is a spatio-temporal extension of traditional tests from the system identification literature and finds applications in similar, yet more general, application scenarios involving graph signals. The AZ-test is versatile, allowing the underlying graph to be dynamic, changing in topology and set of nodes, and weighted, thus accounting for connections of different strength, as is the case in many application scenarios like transportation networks and sensor grids. The asymptotic distribution -- as the number of graph edges or temporal observations increases -- is known, and does not assume identically distributed data. We validate the practical value of the test on both synthetic and real-world problems, and show how the test can be employed to assess the quality of spatio-temporal forecasting models by analyzing the prediction residuals appended to the graphs stream.