History state formalism for time series with application to finance

TL;DR

This paper introduces a quantum-inspired formalism for analyzing time series, especially financial data, using history states and entanglement measures to characterize evolution and volatility.

Contribution

It applies quantum history state formalism to time series analysis, providing new measures like entanglement entropy for understanding data evolution.

Findings

Different evolution regimes identified via entanglement spectrum

Entanglement-based volatility indicators compared with standard measures

Formalism successfully applied to financial time-series data

Abstract

We present a method for analyzing general time series by employing the history state formalism of quantum mechanics. This formalism allows us to describe a complete evolution based on a single quantum state, the history state, which simultaneously includes -also as a quantum system- the reference clock. It naturally leads to the concept of system-time entanglement, with the ensuing entanglement entropy constituting a measure of the effective number of distinguishable states visited in the history. Through a quantum coherent state embedding of the time series data, it is then possible to associate a quantum history state to the series. The gaussian overlap between these coherent states provides thus a smooth measure of distinguishability between the series data. The eigenvalues of the corresponding overlap matrix determine in fact the entanglement spectrum and entropy of the history state, which provide a rigorous characterization of the evolution. As illustration, the formalism is applied to typical financial time-series data. Through the entanglement entropy and spectrum, different evolution regimes can be identified. Entanglement based volatility indicators are also derived, and compared with standard volatility measures.