Economic Accelerator with Memory: Discrete Time Approach

TL;DR

This paper introduces a discrete time model for economic accelerators with power-law memory, derived from fractional differential equations, capturing economic dynamics with memory effects and periodic shocks.

Contribution

It develops a novel discrete map with memory for economic accelerators, bridging fractional calculus and discrete economic modeling without approximations.

Findings

Discrete maps with memory effectively model economic processes.

The approach captures sharp economic shocks and long-term memory effects.

Provides a new framework linking fractional calculus to economic dynamics.

Abstract

Accelerators with power-law memory are proposed in the framework of the discrete time approach. To describe discrete accelerators we use the capital stock adjustment principle, which has been suggested by Matthews.The suggested discrete accelerators with memory describe the economic processes with the power-law memory and the periodic sharp splashes (kicks). In continuous time approach the memory is described by fractional-order differential equations. In discrete time approach the accelerators with memory are described by discrete maps with memory, which are derived from the fractional-order differential equation without approximations. In order to derive these maps we use the equivalence of fractional-order differential equations and the Volterra integral equations.