# On tracking varying bounds when forecasting bounded time series

arXiv: https://arxiv.org/abs/2306.13428 · HTML: https://mlsanity.com/paper/2306.13428/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 36 references that are in the map.
- First posted on arXiv 23 Jun 2023.

## Builds on (most cited first, 3 of 3)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Beyond Convexity: Stochastic Quasi-Convex Optimization](https://mlsanity.com/paper/1507.02030/) (2015)

## Built on by (most cited first, 1 of 1)

- [OpenTSLM TeeMoE: A Unified Time-Series Language Model for Forecasting, Contextual Prediction, and Reasoning](https://mlsanity.com/paper/2609.40265/) (2026)

## Abstract (arXiv)

We consider a new framework where a continuous, though bounded, random variable has unobserved bounds that vary over time. In the context of univariate time series, we look at the bounds as parameters of the distribution of the bounded random variable. We introduce an extended log-likelihood estimation and design algorithms to track the bound through online maximum likelihood estimation. Since the resulting optimization problem is not convex, we make use of recent theoretical results on Normalized Gradient Descent (NGD) for quasiconvex optimization, to eventually derive an Online Normalized Gradient Descent algorithm. We illustrate and discuss the workings of our approach based on both simulation studies and a real-world wind power forecasting problem.