# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1907.05949