Periodic linear discrete multitime diagonal recurrence with application in economics

TL;DR

This paper extends Floquet theory to multitime diagonal recurrences, simplifying their analysis and applying it to economic models to derive meaningful bivariate sequences and their properties.

Contribution

It introduces a Floquet theory extension for multitime diagonal recurrences and applies it to economic models, providing explicit solutions and eigenvalue analysis.

Findings

Explicit monodromy matrix and Floquet multipliers derived

Reduced complex recurrences to simpler constant coefficient systems

Generated functions and multipliers identified for economic models

Abstract

Floquet theory, first published in 1883 for periodic linear differential equations, is extended in this paper to multitime diagonal recurrences. We find explicitly a monodromy matrix, and we comment its eigenvalues (called Floquet multipliers). The Floquet point of view brings about an important simplification: the initial linear diagonal recurrence system is reduced to a linear recurrence system, with constant coefficients along "diagonal lines". The results are applied to the discrete multitime Samuelson-Hicks models, with constant, respectively multi-periodic, coefficients, in order to find bivariate sequences with economic meaning. For constant coefficients case, it was found also the generating function; for multi-periodic coefficients case, we determined the Floquet multipliers.