Predictors for discrete time processes with energy decay on higher frequencies

TL;DR

This paper introduces predictors for discrete-time processes with energy decay at higher frequencies, enabling highly accurate and noise-robust one-step-ahead predictions in a deterministic setting.

Contribution

It proposes a family of predictors tailored for processes with high-frequency energy decay, improving prediction accuracy and robustness.

Findings

Prediction error can be made arbitrarily small.

Predictions are robust to noise at higher frequencies.

Applicable to deterministic processes with energy decay.

Abstract

The predictability of discrete-time processes is studied in a deterministic setting. A family of one-step-ahead predictors is suggested for processes of which the energy decays at higher frequencies. For such processes, the prediction error can be made arbitrarily small. The predictions can be robust with respect to the noise contamination at higher frequencies.