Probabilistic prediction of the AL index with the diffusion forecasting model

TL;DR

This paper introduces a nonparametric probabilistic forecasting method for the AL index using diffusion forecasting, which models the underlying stochastic dynamics from data and provides skillful predictions up to two hours ahead.

Contribution

It presents a novel application of diffusion forecasting with Bayesian filtering for AL index prediction, leveraging data-driven representations of the system's probability evolution.

Findings

Forecasts are skillful up to two hours ahead.

The method handles data gaps effectively.

No exogenous inputs are required for predictions.

Abstract

We propose a nonparametric approach for probabilistic prediction of the AL index trained with AL and solar wind ($v B_z$) data. Our framework relies on the diffusion forecasting technique, which views AL and $ v B_z $ data as observables of an autonomous, ergodic, stochastic dynamical system operating on a manifold. Diffusion forecasting builds a data-driven representation of the Markov semigroup governing the evolution of probability measures of the dynamical system. In particular, the Markov semigroup operator is represented in an orthonormal basis acquired from data using the diffusion maps algorithm and Takens delay embeddings. This representation of the evolution semigroup is used in conjunction with a Bayesian filtering algorithm for forecast initialization to predict the probability that the AL index is less than a user-selected threshold over arbitrary lead times and without requiring exogenous inputs. We find that the model produces skillful forecasts out to at least two-hour leads despite gaps in the training data.