An autoregressive approach to modeling commodity prices as a quasi-fractional Brownian motion
Abstract
Purpose
The purpose of this paper is to argue that a stationary-differenced autoregressive (AR) process with lag greater than 1, AR(q > 1), has certain properties that are consistent with a fractional Brownian motion (fBm). What the authors are interested in is the investigation of approaches to identifying the existence of persistent memory of one form or another for the purposes of simulating commodity (and other asset) prices. The authors show in theory, and with application to agricultural commodity prices the relationship between AR(q) and quasi-fBm.
Design/methodology/approach
In this paper the authors develop mathematical relationships in support of using AR(q > 1) processes for simulating quasi-fBm.
Findings
From theory the authors show that any AR(q) process is a stationary, self-similar process, with a lag structure that captures the essential elements of scaling and a fractional power law. The authors illustrate through various means the approach, and apply the quasi-fractional AR(q) process to agricultural commodity prices.
Research limitations/implications
While the results can be applied to most time series of commodity prices, the authors limit the evaluation to the Gaussian case. Thus the approach does not apply to infinite-variance models.
Practical implications
The approach to using the structure of an AR(q > 1) model to simulate quasi-fBm is a simple approach that can be applied with ease using conventional Monte Carlo methods.
Originality/value
The authors believe that the approach to simulating quasi-fBm using standard AR(q > 1) models is original. The approach is intuitive and can be applied easily.
Keywords
Acknowledgements
This paper was derived from Paitoon Wongsasutthikul ' s PhD dissertation, Hurst Trading with an Excursion into Fractal Space of Returns, Cornell University, January 2012. The authors are thankful for funds made available from the W.I. Myers endowment in support of this paper. This paper was first presented at the IARFIC conference, Washington DC, June 2015. The authors are especially grateful to the very helpful detailed reviews and comments from Hirbod Assa (University of Liverpool), Gabriel Power (Laval University) and Tom Sproul (University of Rhode Island). All errors and omissions, etc. are the responsibility of the authors (and in particular, Turvey).
Citation
Turvey, C.G. and Wongsasutthikul, P. (2016), "An autoregressive approach to modeling commodity prices as a quasi-fractional Brownian motion", Agricultural Finance Review, Vol. 76 No. 1, pp. 54-75. https://doi.org/10.1108/AFR-01-2016-0004
Publisher
:Emerald Group Publishing Limited
Copyright © 2016, Emerald Group Publishing Limited