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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.

In this paper the authors develop mathematical relationships in support of using AR(q > 1) processes for simulating quasi-fBm.

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.

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.

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.

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.