Autoregressive with Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Series

TL;DR

This paper introduces the ARS model, a novel approach for forecasting partially observed dynamical time series by jointly estimating the evolution function and imputing missing variables, supported by theoretical reconstruction guarantees.

Contribution

The paper proposes the autoregressive with slack time series (ARS) model that handles missing variables in dynamical systems and provides theoretical reconstruction results for linear systems.

Findings

ARS accurately forecasts future time series with missing data.

Theoretical proof of reconstructing 2D linear systems from partial observations.

Model demonstrates robustness in partially observed dynamical systems.

Abstract

This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by inferring the evolution function. However, these methods may confront obstacles due to the presence of missing variables, which are usually attributed to challenges in measurement and a partial understanding of the system of interest. To overcome this obstacle, we introduce the autoregressive with slack time series (ARS) model, that simultaneously estimates the evolution function and imputes missing variables as a slack time series. Assuming time-invariance and linearity in the (underlying) entire dynamical time series, our experiments demonstrate the ARS model's capability to forecast future time series. From a theoretical perspective, we prove that a 2-dimensional time-invariant and linear system can be reconstructed by utilizing observations from a single, partially observed dimension of the system.