Bridging the Gap: Decoding the Intrinsic Nature of Time in Market Data

TL;DR

This paper uncovers a fundamental link between intrinsic event-based time and physical clock time in financial data, revealing scaling laws and enabling decomposition of market dynamics into liquidity and volatility components.

Contribution

It introduces an analytic relationship connecting intrinsic and physical time, supported by empirical scaling laws and analysis of diverse financial time series.

Findings

Derived a new scaling law for overshoot variability in intrinsic time.

Validated the relationship using Brownian motion and currency market data.

Demonstrated decomposition of market data into liquidity and volatility components.

Abstract

Intrinsic time is an example of an event-based conception of time, used to analyze financial time series. Here, for the first time, we reveal the connection between intrinsic time and physical time. In detail, we present an analytic relationship which links the two different time paradigms. Central to this discovery are the emergence of scaling laws. Indeed, a novel empirical scaling law is presented, relating to the variability of what is know as overshoots in the intrinsic time framework. To evaluate the validity of the theoretically derived expressions, three time series are analyzed; in detail, Brownian motion and two tick-by-tick empirical currency market data sets (one crypto and one fiat). Finally, the time series analyzed in physical time can be decomposed into their liquidity and volatility components, both only visible in intrinsic time, further highlighting the utility of this temporal kinship.