Predictability on finite horizon for processes with exponential decrease of energy on higher frequencies

TL;DR

This paper establishes conditions under which processes with exponential energy decay at higher frequencies are predictable over finite horizons, providing explicit predictor formulas and demonstrating uniform predictability across process classes.

Contribution

It introduces new sufficient conditions for predictability of processes with exponential spectral decay and offers explicit predictor formulas in a deterministic setting.

Findings

Processes with exponential spectral decay are predictable over finite horizons.

Predictability can be achieved uniformly across classes of such processes.

Explicit formulas for predictors are provided.

Abstract

The paper presents sufficient conditions of predictability for continuous time processes in deterministic setting. We found that processes with exponential decay on energy for higher frequencies are predictable in some weak sense on some finite time horizon defined by the rate of decay. Moreover, this predictability can be achieved uniformly over classes of processes. Some explicit formulas for predictors are suggested.