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Generative Probabilistic Time Series Forecasting and Applications in Grid Operations

Xinyi Wang, Lang Tong, Qing Zhao

TL;DR

It is shown that the weak innovation sequence is Bayesian sufficient, which makes the proposed weak innovation autoencoder a canonical architecture for generative probabilistic forecasting.

Abstract

Generative probabilistic forecasting produces future time series samples according to the conditional probability distribution given past time series observations. Such techniques are essential in risk-based decision-making and planning under uncertainty with broad applications in grid operations, including electricity price forecasting, risk-based economic dispatch, and stochastic optimizations. Inspired by Wiener and Kallianpur's innovation representation, we propose a weak innovation autoencoder architecture and a learning algorithm to extract independent and identically distributed innovation sequences from nonparametric stationary time series. We show that the weak innovation sequence is Bayesian sufficient, which makes the proposed weak innovation autoencoder a canonical architecture for generative probabilistic forecasting. The proposed technique is applied to forecasting highly volatile real-time electricity prices, demonstrating superior performance across multiple forecasting measures over leading probabilistic and point forecasting techniques.

Generative Probabilistic Time Series Forecasting and Applications in Grid Operations

TL;DR

It is shown that the weak innovation sequence is Bayesian sufficient, which makes the proposed weak innovation autoencoder a canonical architecture for generative probabilistic forecasting.

Abstract

Generative probabilistic forecasting produces future time series samples according to the conditional probability distribution given past time series observations. Such techniques are essential in risk-based decision-making and planning under uncertainty with broad applications in grid operations, including electricity price forecasting, risk-based economic dispatch, and stochastic optimizations. Inspired by Wiener and Kallianpur's innovation representation, we propose a weak innovation autoencoder architecture and a learning algorithm to extract independent and identically distributed innovation sequences from nonparametric stationary time series. We show that the weak innovation sequence is Bayesian sufficient, which makes the proposed weak innovation autoencoder a canonical architecture for generative probabilistic forecasting. The proposed technique is applied to forecasting highly volatile real-time electricity prices, demonstrating superior performance across multiple forecasting measures over leading probabilistic and point forecasting techniques.
Paper Structure (12 sections, 1 theorem, 8 equations, 4 figures, 1 table)

This paper contains 12 sections, 1 theorem, 8 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Summary of Contributions
  3. A Contextual Review of Literature
  4. Innovation Representation
  5. Generative Probabilistic Forecasting
  6. GPF with Weak Innovation
  7. Weak Innovation are Bayesian Sufficient
  8. Learning Innovation Representation
  9. Numerical Results
  10. Electricity Prices and Datasets
  11. Results
  12. Conclusion

Key Result

Theorem 1

Let $(X_t)$ be a stationary time series for which the weak innovation exists. Let $(V_t)$ be the weak innovation sequence of $(X_t)$, and assume that the causal decoder $H$ is injective. Then, for almost all ${\bm x}_t$ and $x$ (with respect to Lebesgue measure), where $F_{t+T|t}(x|{\bm x}_t)$ is defined in eq:conditional_prob, $\hbox{\boldmath$\nu$\unboldmath}_t=G({\bm x}_t)$, and

Figures (4)

  • Figure 1: An autoencoder interpretation of innovation representation.
  • Figure 2: Probabilistic Forecasting via Weak Innovations.
  • Figure 3: Training WIAE with discriminators.
  • Figure 4: Trajectory of ISONE real-time electricity price.

Theorems & Definitions (1)

  • Theorem 1: Bayesian Sufficiency