Autoregressive with Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Series
This addresses forecasting challenges in dynamical systems for researchers dealing with partially observed data, but it is incremental as it builds on traditional methods with specific assumptions.
The paper tackles forecasting of dynamical time series with missing variables by introducing the ARS model, which simultaneously estimates the evolution function and imputes missing data, and demonstrates its capability to forecast future time series in experiments.
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.