On the residues vectors of a rational class of complex functions. Application to autoregressive processes

TL;DR

This paper studies the residues of a specific class of rational complex functions, deriving properties and bounds, and applies these findings to analyze autoregressive processes in fields like energy and economics.

Contribution

It introduces new bounds on the p-norm of residues vectors for a class of rational functions and applies these results to autoregressive process analysis.

Findings

Established a lower bound for the p-norm of residues vectors.

Applied theoretical results to real-world electric and econometric data.

Demonstrated relevance of residues analysis in autoregressive process modeling.

Abstract

Complex functions have multiple uses in various fields of study, so analyze their characteristics it is of extensive interest to other sciences. This work begins with a particular class of rational functions of a complex variable; over this is deduced two elementals properties concerning the residues and is proposed one results which establishes one lower bound for the p-norm of the residues vector. Applications to the autoregressive processes are presented and the exemplifications are indicated in historical data of electric generation and econometric series.