Determine the optimal sparse observation interval Δt

Determine an optimal choice of the fixed interval length Δt used in the sparse observation preprocessing of high-frequency mid-price data, wherein for each multiple nΔt the procedure records the last time before nΔt at which the price equals P(nΔt) and skips periods with no change.

Background

To mitigate microstructure noise, the paper proposes a sparse preprocessing method that, for each multiple of a fixed interval Δt, records the last time prior to that multiple when the price equals its value at the multiple and omits repeated values. The choice of Δt directly affects the resulting point process used for model estimation and simulation.

The authors note that Δt is chosen subjectively in their experiments and explicitly acknowledge that the optimal interval is unknown, motivating the need for a principled selection procedure.