# Non-parametric Probabilistic Time Series Forecasting via Innovations Representation

arXiv: https://arxiv.org/abs/2306.03782 · HTML: https://mlsanity.com/paper/2306.03782/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 15 of 15)

- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Conditional Time Series Forecasting with Convolutional Neural Networks](https://mlsanity.com/paper/1703.04691/) (2017)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [GluonTS: Probabilistic Time Series Models in Python](https://mlsanity.com/paper/1906.05264/) (2019)
- [Learning Independent Features with Adversarial Nets for Non-linear ICA](https://mlsanity.com/paper/1710.05050/) (2017)
- [Temporal Latent Auto-Encoder: A Method for Probabilistic Multivariate Time Series Forecasting](https://mlsanity.com/paper/2101.10460/) (2021)
- [Robust Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.11910/) (2022)
- [Innovations Autoencoder and its Application in One-class Anomalous Sequence Detection](https://mlsanity.com/paper/2106.12382/) (2021)
- [Synergetic Learning of Heterogeneous Temporal Sequences for Multi-Horizon Probabilistic Forecasting](https://mlsanity.com/paper/2102.00431/) (2021)

## Built on by (most cited first, 2 of 2)

- [Mamba time series forecasting with uncertainty quantification](https://mlsanity.com/paper/2503.10873/) (2025)
- [Generative Probabilistic Time Series Forecasting and Applications in Grid Operations](https://mlsanity.com/paper/2402.13870/) (2024)

## Abstract (arXiv)

Probabilistic time series forecasting predicts the conditional probability distributions of the time series at a future time given past realizations. Such techniques are critical in risk-based decision-making and planning under uncertainties. Existing approaches are primarily based on parametric or semi-parametric time-series models that are restrictive, difficult to validate, and challenging to adapt to varying conditions. This paper proposes a nonparametric method based on the classic notion of em innovations pioneered by Norbert Wiener and Gopinath Kallianpur that causally transforms a nonparametric random process to an independent and identical uniformly distributed em innovations process. We present a machine-learning architecture and a learning algorithm that circumvent two limitations of the original Wiener-Kallianpur innovations representation: (i) the need for known probability distributions of the time series and (ii) the existence of a causal decoder that reproduces the original time series from the innovations representation. We develop a deep-learning approach and a Monte Carlo sampling technique to obtain a generative model for the predicted conditional probability distribution of the time series based on a weak notion of Wiener-Kallianpur innovations representation. The efficacy of the proposed probabilistic forecasting technique is demonstrated on a variety of electricity price datasets, showing marked improvement over leading benchmarks of probabilistic forecasting techniques.