**This is a summary of a research project I participated in. I’m reproducing
the introduction and results here, but see the full PDF
for the method, more detailed results, and extra figures.**

# Introduction

This project aims to study the evolutions in the structure of transaction sign autocorrelation on electronic stock markets between 2000 and 2013. Previous works on this topic, based on data from the first half of the 2000’s, describe a very long memory of these signs (with a power-law decrease of autocorrelation). It is then natural to ask whether the massive rise of high-frequency trading and automated execution strategies have induced significant evolutions of this structure.

The high-frequency data used to conduct this study was provided by the Chair of Quantitative Finance at CentraleSupélec.

# Results

## Study of the decrease in autocorrelation

Lillo found the trade sign autocorrelation of the Vodaphone stock on the LSE in 2004 to be significant up to a lag of $10^4$. For the Total stock, we find a coherent autocorrelation up to about $3\cdot 10^3$ in 2005 et $10^3$. However the noise level is significant after a lag of 500, especially after averaging all stocks in our study (which includes stocks far less liquid, and thus far more noisy, than Total). For the remainder of this study, we have focused on lags up to 300.

With both methods of averaging (over several stocks or over one stock), we can observe a significant evolution starting in 2010. Until 2009, autocorrelation follows a power law. From 2010 on, autocorrelations can be described with two successive power laws of differing exponents, changing around $t=10$.

These results are clearly visible on double logarithmic scale plots: in this scale, trade sign autocorrelations form a straight line until 2009, then angle. This phenomenon is visible on both methods of averaging. Using a linear regression on the log-log plots, one finds an exponent of $\gamma \approx 0.28$ to $0.38$ up to 2009, then about $\gamma \approx 0.50$ to $0.60$ on the first piece and $\gamma \approx 0.17$ to $0.20$ on the second. At a lag of 300, autocorrelation is approximatively equal for all years (to about $10^{-2}$). At a lag of 10, however, it is equal to about $5\cdot 10^{-2}$ for 2010-2013, contrasting with a value of $10^{-1}$ for the 2000-2009 period.

These variations can also bee seen on relative volume time plots. Physical time plots (with 60 second segments) suffer from higher noise; the break in slope is not clearly visible, but autocorrelation at lag 2 is much higher in 2010-2013 than before. The following slope is also less steep.

Overall, this change is relatively intriguing: in the later years, the initial decrease is much faster but is compensated at larger lags by a slower decrease of the tail.

## Analysis

The most significant changes on financial markets since 2007-2008 are without doubt market deregulation and the growing share of algorithmic trading in exchanges. The impact of these changes can be relatively ambiguous: high-frequency trading, for instance, will tend to cause a large amount of trades, which depending on the algorithm can be of correlated signs or not.

Deregulation allows more actors to trade on the exchanges and have an impact on trade signs. Trade sign autocorrelation may then have a steeper decrease because of this increased liquidity.

Additionally, the growing role of algorithmic trading (in 2008, on the German stock exchange, 50 to 60% of all traded volume was due to algorithmic trading). This also adds liquidity to the market, and possibly noise because of the large number of trades.

In any case, it remains difficult to explain why the power law exponent grows in the second phase.