Generative Probabilistic Time Series Forecasting and Applications in Grid Operations (2402.13870v1)

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.

• The paper introduces the GPF-WI framework that leverages weak innovation autoencoders to extract independent innovation sequences for nonparametric time series forecasting.
• The methodology employs Bayesian sufficiency, ensuring that decisions based solely on weak innovations remain optimal under uncertainty.
• Application to volatile real-time electricity pricing shows superior forecasting accuracy compared to traditional probabilistic and point forecasting techniques.

Generative Probabilistic Forecasting via Weak Innovation Autoencoders: A New Pathway in Time Series Analysis

Introduction to Generative Probabilistic Forecasting

Generative Probabilistic Forecasting (GPF) emerges as a pivotal technique in addressing the challenges innate to decision-making under uncertainty, especially in grid operations. This technique hinges on generating future time series samples based on the conditional probability distribution given past observations. Traditional approaches often resort to parametric models, limiting their effectiveness in capturing the full spectrum of complexities in nonparametric time series models. Venturing into the field of nonparametric probabilistic forecasting introduces the concept of a weak innovation autoencoder (WIAE) inspired by the foundational work of Wiener and Kallianpur on innovation representation.

Weak Innovation Autoencoder (WIAE)

WIAE stands as a cornerstone in our approach to GPF. It mitigates the challenges posed by nonparametric time series forecasting by extracting identically distributed innovation sequences from stationary time series. Through its architecture, the WIAE distills new information at each time step, independent of past observations, encapsulating it in what is referred to as the weak innovation sequence. This procedure not only broadens the scope of applicable time series beyond what strong innovation representation permits but also upholds the Bayesian sufficiency for generative probabilistic forecasting.

Generative Probabilistic Forecasting with Weak Innovation (GPF-WI)

GPF-WI is introduced as a potent method to operationalize the concept of WIAE in time series forecasting. Rather than attempting to directly generate samples from the conditional distribution, which is computationally intractable, GPF-WI cleverly leverages past innovation observations along with independently sampled data. This methodological innovation simplifies the process considerably, relying on the decoder's capacity to utilize past innovations for future predictions.

Theoretical Implications and Bayesian Sufficiency

One of the theoretical bedrocks of this paper is the establishment of Bayesian sufficiency for weak innovation sequences in the context of probabilistic forecasting. The implication here is profound: decisions made based on weak innovation sequences do not result in a loss of optimality. This theoretical underpinning validates the use of WIAE in generative forecasting, ensuring that the forecasts generated are not only credible but also optimal from a Bayesian perspective.

Practical Applications and Performance Evaluation

The practical significance of the proposed GPF-WI technique is underscored through its application to forecasting highly volatile real-time electricity prices. The empirical evaluation across various datasets showcases the method's superior performance in probabilistic forecasting measures compared to existing probabilistic and point forecasting techniques. This empirical evidence not only validates the efficacy of GPF-WI but also emphasizes its potential in improving decision-making processes in grid operations and beyond.

Concluding Remarks

The exploration of generative probabilistic forecasting through weak innovation autoencoders opens new avenues in the analysis of nonparametric time series. By leveraging the Bayesian sufficiency of weak innovation sequences, the proposed GPF-WI technique sets a new standard in forecasting, particularly in scenarios characterized by high volatility and uncertainty. The implications of this research extend far beyond grid operations, promising advancements in various fields where decision-making under uncertainty is paramount. As we progress, the adaptability and potential extensions of WIAE, including its application to multivariate time series, and the exploration of advanced neural network architectures, herald a promising future in the field of generative probabilistic forecasting.