  Order flow in equity markets is remarkably persistent in the sense that order
signs (to buy or sell) are positively autocorrelated out to time lags of tens
of thousands of orders, corresponding to many days. Two possible explanations
are herding, corresponding to positive correlation in the behavior of different
investors, or order splitting, corresponding to positive autocorrelation in the
behavior of single investors. We investigate this using order flow data from
the London Stock Exchange for which we have membership identifiers. By
formulating models for herding and order splitting, as well as models for
brokerage choice, we are able to overcome the distortion introduced by
brokerage. On timescales of less than a few hours the persistence of order flow
is overwhelmingly due to splitting rather than herding. We also study the
properties of brokerage order flow and show that it is remarkably consistent
both cross-sectionally and longitudinally.
