Mixed Models as an Alternative to Farima

TL;DR

The paper introduces a new process combining fractional Brownian motion and fractional Ornstein-Uhlenbeck processes, offering a simpler alternative to FARIMA with comparable autocovariance and easier variance computation.

Contribution

It proposes a novel process that approximates FARIMA autocovariance structures with simplified variance calculations, expanding modeling options.

Findings

The new process has similar autocovariance to FARIMA.

Variance of the increment process has a closed-form expression.

The model is more parsimonious and computationally efficient.

Abstract

We construct a new process using a fractional Brownian motion and a fractional Ornstein-Uhlenbeck process of the Second Kind as building blocks. We consider the increments of the new process in discrete time and, as a result, we obtain a more parsimonious process with similar autocovariance structure to that of a FARIMA. In practice, variance of the new increment process is a closed-form expression easier to compute than that of FARIMA.