# Time series forecasting with Gaussian Processes needs priors

arXiv: https://arxiv.org/abs/2009.08102 · HTML: https://mlsanity.com/paper/2009.08102/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2020.

## Built on by (most cited first, 13 of 13)

- [Conformal Prediction for Time Series with Modern Hopfield Networks](https://mlsanity.com/paper/2303.12783/) (2023)
- [Learning Deep Time-index Models for Time Series Forecasting](https://mlsanity.com/paper/2207.06046/) (2022)
- [SSD-TS: Exploring the Potential of Linear State Space Models for Diffusion Models in Time Series Imputation](https://mlsanity.com/paper/2410.13338/) (2024)
- [Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representations](https://mlsanity.com/paper/2306.05880/) (2023)
- [Time Series Forecasting Using Manifold Learning](https://mlsanity.com/paper/2110.03625/) (2021)
- [Correlated Product of Experts for Sparse Gaussian Process Regression](https://mlsanity.com/paper/2112.09519/) (2021)
- [Sequential Monte Carlo Learning for Time Series Structure Discovery](https://mlsanity.com/paper/2307.09607/) (2023)
- [Fully Bayesian Differential Gaussian Processes through Stochastic Differential Equations](https://mlsanity.com/paper/2408.06069/) (2024)
- [dynoGP: Deep Gaussian Processes for dynamic system identification](https://mlsanity.com/paper/2502.05620/) (2025)
- [Forecasting intermittent time series with Gaussian Processes and Tweedie likelihood](https://mlsanity.com/paper/2502.19086/) (2025)
- [DynaConF: Dynamic Forecasting of Non-Stationary Time Series](https://mlsanity.com/paper/2209.08411/) (2022)
- [MoTM: Towards a Foundation Model for Time Series Imputation based on Continuous Modeling](https://mlsanity.com/paper/2507.13207/) (2025)
- [Time Series Imputation with Multivariate Radial Basis Function Neural Network](https://mlsanity.com/paper/2407.17040/) (2024)

## Abstract (arXiv)

Automatic forecasting is the task of receiving a time series and returning a forecast for the next time steps without any human intervention. Gaussian Processes (GPs) are a powerful tool for modeling time series, but so far there are no competitive approaches for automatic forecasting based on GPs. We propose practical solutions to two problems: automatic selection of the optimal kernel and reliable estimation of the hyperparameters. We propose a fixed composition of kernels, which contains the components needed to model most time series: linear trend, periodic patterns, and other flexible kernel for modeling the non-linear trend. Not all components are necessary to model each time series; during training the unnecessary components are automatically made irrelevant via automatic relevance determination (ARD). We moreover assign priors to the hyperparameters, in order to keep the inference within a plausible range; we design such priors through an empirical Bayes approach. We present results on many time series of different types; our GP model is more accurate than state-of-the-art time series models. Thanks to the priors, a single restart is enough the estimate the hyperparameters; hence the model is also fast to train.