# Inferring serial correlation with dynamic backgrounds

arXiv: https://arxiv.org/abs/2101.10962 · HTML: https://mlsanity.com/paper/2101.10962/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jan 2021.

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

- [Weather-Informed Probabilistic Forecasting and Scenario Generation in Power Systems](https://mlsanity.com/paper/2409.07637/) (2024)
- [Online Kernel CUSUM for Change-Point Detection](https://mlsanity.com/paper/2211.15070/) (2022)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2301.11197/) (2023)
- [Causal Graph Discovery from Self and Mutually Exciting Time Series](https://mlsanity.com/paper/2106.02600/) (2021)
- [Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models](https://mlsanity.com/paper/2305.18578/) (2023)

## Abstract (arXiv)

Sequential data with serial correlation and an unknown, unstructured, and dynamic background is ubiquitous in neuroscience, psychology, and econometrics. Inferring serial correlation for such data is a fundamental challenge in statistics. We propose a total variation constrained least square estimator coupled with hypothesis tests to infer the serial correlation in the presence of unknown and unstructured dynamic background. The total variation constraint on the dynamic background encourages a piece-wise constant structure, which can approximate a wide range of dynamic backgrounds. The tuning parameter is selected via the Ljung-Box test to control the bias-variance trade-off. We establish a non-asymptotic upper bound for the estimation error through variational inequalities. We also derive a lower error bound via Fano's method and show the proposed method is near-optimal. Numerical simulation and a real study in psychology demonstrate the excellent performance of our proposed method compared with the state-of-the-art.