Optimal data recovery and forecasting with dummy long-horizon forecasts

TL;DR

This paper introduces a method for recovering missing data in sequences using spectrum degeneracy, which improves forecasting accuracy by regularizing solutions with dummy long-horizon forecasts, without relying on probabilistic assumptions.

Contribution

It presents a novel deterministic approach for data recovery and forecasting that leverages spectrum degeneracy and dummy long-horizon forecasts for regularization.

Findings

The method effectively recovers missing data in multidimensional sequences.

It demonstrates robustness to noise contamination.

The approach improves long-horizon forecasting accuracy.

Abstract

The paper suggests a method of recovering missing values for sequences, including sequences with a multidimensional index, based on optimal approximation by processes featuring spectrum degeneracy. The problem is considered in the pathwise setting, without using probabilistic assumptions on the ensemble. The method requires to solve a closed linear equation connecting the available observations of the underlying process with the values of the approximating process with degenerate spectrum outside the observation range.Some robustness with respect to noise contamination is established for the suggested recovering algorithm. It is suggested to apply this data recovery algorithm to forecasting with a preselected dummy long-horizon forecast that helps to regularize the solution.