Non-parametric Probabilistic Time Series Forecasting via Innovations Representation

• URL: http://arxiv.org/abs/2306.03782v1
• Date: Mon, 5 Jun 2023 02:24:59 GMT
• Title: Non-parametric Probabilistic Time Series Forecasting via Innovations Representation
• Authors: Xinyi Wang, Meijen Lee, Qing Zhao, Lang Tong
• Abstract summary: Probabilistic time series forecasting predicts the conditional probability distributions of the time series at a future time given past realizations. 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.
• Score: 29.255644836978956
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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