On causal extrapolation of sequences with applications to forecasting

TL;DR

This paper introduces a novel method for causal extrapolation and forecasting of sequences, ensuring unique predictions through semi-infinite sequence analysis and mean square error minimization, applicable to a broad class of sequences.

Contribution

It presents a new extrapolation technique based on semi-infinite sequences and a forecasting method using mean square error minimization, extending applicability beyond band-limited sequences.

Findings

Ensures unique extrapolation of sequences.

Provides a causal smoothing interpretation.

Enables optimal forecasting for general sequences.

Abstract

The paper suggests a method of extrapolation of notion of one-sided semi-infinite sequences representing traces of two-sided band-limited sequences; this features ensure uniqueness of this extrapolation and possibility to use this for forecasting. This lead to a forecasting method for more general sequences without this feature based on minimization of the mean square error between the observed path and a predicable sequence. These procedure involves calculation of this predictable path; the procedure can be interpreted as causal smoothing. The corresponding smoothed sequences allow unique extrapolations to future times that can be interpreted as optimal forecasts.