Construct a meaningful waiting-time distribution for the OBD-II time series

Construct a meaningful waiting-time distribution for the continuous two-dimensional time series of vehicle speed and engine RPM sampled approximately every 140 ms from Automobilus subaru via the OBD-II port, in order to enable application of the Skinner–Dunkel waiting-time–based entropy production estimator to these data.

Background

The paper surveys multiple estimators and bounds for entropy production, including a waiting-time–based approach introduced by Skinner and Dunkel that is suitable when only coarse-grained state occupancy and waiting-time information are available. This method requires defining a waiting-time distribution from observed data.

The dataset analyzed here consists of two continuous observables (vehicle speed and engine RPM) recorded from a car’s OBD-II port at roughly 140 ms intervals. Unlike discrete two-state trajectories (e.g., a metronome being left or right of center), it is nontrivial to define events and associated residence times from these continuous variables. The authors note they cannot determine a meaningful waiting-time distribution for their dataset, preventing application of the waiting-time estimator.

References

However, it's not clear how to produce a meaningful waiting time distribution from our dataset.

— In-vivo entropy production of A. subaru  (2604.00453 - Fu et al., 1 Apr 2026) in Results, paragraph discussing the Skinner–Dunkel waiting-time estimator (following the discussion of alternative EPR approaches)