# Theory and Algorithms for Forecasting Time Series

arXiv: https://arxiv.org/abs/1803.05814 · HTML: https://mlsanity.com/paper/1803.05814/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2018.

## Built on by (most cited first, 7 of 7)

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- [Tempo Adaptation in Non-stationary Reinforcement Learning](https://mlsanity.com/paper/2309.14989/) (2023)
- [Learning Ergodic Dynamical Systems from a Finite Trajectory](https://mlsanity.com/paper/2607.22399/) (2026)
- [Smart Predict-then-Optimize Method with Dependent Data: Risk Bounds and Calibration of Autoregression](https://mlsanity.com/paper/2411.12653/) (2024)
- [A Memory Efficient Unified Algorithm for Online Learning of Linear Dynamical Systems](https://mlsanity.com/paper/2607.02050/) (2026)

## Abstract (arXiv)

We present data-dependent learning bounds for the general scenario of non-stationary non-mixing stochastic processes. Our learning guarantees are expressed in terms of a data-dependent measure of sequential complexity and a discrepancy measure that can be estimated from data under some mild assumptions. We also also provide novel analysis of stable time series forecasting algorithm using this new notion of discrepancy that we introduce. We use our learning bounds to devise new algorithms for non-stationary time series forecasting for which we report some preliminary experimental results.