I just came across this interesting study of long-term memory in a stock market.
Using data from the London Stock Exchange we demonstrate that the signs of orders obey a long-memory
process. The autocorrelation function decays roughly as t^(-alpha) with alpha ~ 0.6, corresponding
to a Hurst exponent H ~ 0.7. The time t is measured in terms of the number of intervening events.
This is true for market orders, limit orders, and cancellations. Although the values for alpha vary from
stock to stock, in the range 0.36 - 0.77, in most cases the exponents for different stocks are quite
similar, and they are always less than one. This implies that the signs of future orders are quite
predictable from the signs of past orders; all else being equal, this would suggest a very strong
market inefficiency. We demonstrate, however, that fluctuations in signs are compensated for by
anti-correlated fluctuations in transaction size and liquidity. For example, when buy orders become
more likely, buy orders tend to be smaller than sell orders and buy liquidity tends to be higher than
sell liquidity. By breaking down the data by institutional codes we show that some institutions
display long-range memory and others donâ€™t.
http://www.santafe.edu/sfi/publications ... 12-066.pdf
Discussions specific to trading the stock market.
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