How fast does the clock of Finance run? - A time-definition enforcing scale invariance and quantifying overnights

TL;DR

This paper introduces a symmetry-guided time definition in finance that enforces scale invariance and stationarity, simplifying the analysis of market series and accurately quantifying inactive periods like overnights.

Contribution

It proposes a novel time scale based on symmetry principles that reduces multiscaling and incorporates inactive periods, improving financial data analysis.

Findings

Enforces scale invariance and stationarity in return distributions.

Quantifies inactive periods such as overnight durations.

Provides a parsimonious framework for analyzing financial series.

Abstract

A symmetry-guided definition of time may enhance and simplify the analysis of historical series with recurrent patterns and seasonalities. By enforcing simple-scaling and stationarity of the distributions of returns, we identify a successful protocol of time definition in Finance. The essential structure of the stochastic process underlying the series can thus be analyzed within a most parsimonious symmetry scheme in which multiscaling is reduced in the quest of a time scale additive and independent of moment-order in the distribution of returns. At the same time, duration of periods in which markets remain inactive are properly quantified by the novel clock, and the corresponding (e.g., overnight) returns are consistently taken into account for financial applications.