The Lillo-Mike-Farmer Splitting Model

If you look at the sequence of buy and sell signs in a stock's trade tape, the sign of one trade is a surprisingly good predictor of the sign of trades minutes or even hours later — a long-memory autocorrelation that decays extremely slowly, unlike the fast-decaying autocorrelation of prices themselves. On its face this looks like it should mean strong, persistent information: many traders all learning the same thing and buying (or selling) together for a long stretch.

Lillo, Mike, and Farmer showed a simpler mechanical explanation fits the data at least as well: large institutional orders are routinely broken up into many smaller child orders, executed gradually over minutes to days to avoid moving the price against themselves. If a single "parent" order to buy 500,000 shares gets sliced into hundreds of smaller trades spread over the day, the trade tape will show a long run of same-signed trades that has nothing to do with hundreds of independent informed traders — it is one large decision, mechanically stretched out in time. Because different institutions are splitting different parent orders of different sizes over different, overlapping horizons, the aggregate signature left in the tape is exactly the kind of slowly decaying, long-memory autocorrelation that had previously been read as evidence of persistent information flow.

Their model reproduces the empirically observed decay rate of order-sign autocorrelation using only assumptions about typical parent order sizes and the way traders split them, without needing to assume any information arrival process at all.