Intraday Trades Profile Estimation: An Intensity Approach

The intraday trades profile is the expected intensity of a counting process where the counts measure the number of trades over an interval. It needs to capture the salient features of the trading activity, its spikes, and periods of relative quietness. This calls for an estimator with a time varying resolution that allows us to identify jumps. The problem can be recast as a regression one, using a fused Lasso penalty. The framework allows us to identify jumps within possibly thousands different locations within a day when the number of trading days at disposal is in the order of hundreds. This can be done without imposing any conditions on the counting process except for certain regularity conditions on the expected intensity. The empirical results suggest that much of the trading activity in some liquid futures can be captured by a deterministic seasonal component in the trade arrival process.