A theory for long-memory in supply and demand

TL;DR

This paper presents a theoretical model explaining long-memory effects in financial market order signs and execution rates, linking power law distributed large orders to persistent autocorrelations observed empirically.

Contribution

It introduces a model connecting order splitting and power law order sizes to long-memory autocorrelations in market order signs and execution rates.

Findings

Power law distributed large orders cause long-memory in order signs.

Autocorrelation decays as tau to the power -(alpha - 1).

Model matches empirical long-memory data.

Abstract

Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such large orders is power law distributed, this gives rise to power law decaying autocorrelations in the signs of executed orders. More specifically, we show that if the cumulative distribution of large orders of volume v is proportional to v to the power -alpha and the size of executed orders is constant, the autocorrelation of order signs as a function of the lag tau is asymptotically proportional to tau to the power -(alpha - 1). This is a long-memory process when alpha < 2. With a few caveats, this gives a good match to the data. A version of the model also shows long-memory fluctuations in order execution rates, which may be relevant for explaining the long-memory of price diffusion rates.