Asynchronous observation within the circulation framework

Develop a general treatment of asynchronous observation within the circulation framework for assets observed at different frequencies or asynchronously, beyond the session-alignment procedure designed for markets with defined trading hours.

Background

The paper’s circulation estimator is formulated for comparable series observed on a common time grid. In practical financial and other scientific applications, observations may instead arrive at different frequencies or at asynchronous times. The paper’s current alignment strategy relies on market sessions with defined trading hours and therefore does not provide a general solution for irregularly timed observations.

A general asynchronous-observation treatment would extend the framework to settings in which contemporaneous and lagged relationships must be identified despite nonuniform observation times, mixed sampling frequencies, or partially overlapping records.

References

Assets observed at different frequencies, or asynchronously, are the norm in practice, and the alignment step we use, the session decomposition of Section~\ref{sec:design}, is specific to markets with defined trading hours. A general treatment of asynchronous observation within this framework is open.

— Measuring the Arrow of Time: Identification, Estimation, and Inference for Directional Structure in Multivariate Time Series  (2608.13431 - Bhandari, 13 Aug 2026) in Section 7.4, “Open problems,” subsection “Continuous-time and mixed-frequency records”