# Maximum Entropy approach to multivariate time series randomization

## TL;DR

This paper introduces a data-driven, maximum entropy-based framework for hypothesis testing in complex multivariate time series, addressing challenges of non-stationarity and ergodicity in natural and social systems.

## Contribution

It develops an unsupervised, statistical mechanical approach for creating ensembles of time series that preserve key empirical properties, enabling more robust hypothesis testing.

## Key findings

- Framework successfully applied to financial portfolio analysis
- Enables hypothesis testing without stationarity assumptions
- Provides a new tool for analyzing complex interacting systems

## Abstract

Natural and social multivariate systems are commonly studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis testing: the statistical properties of the empirical time series are tested against those expected under a suitable null hypothesis. This is a very challenging task in complex interacting systems, where statistical stability is often poor due to lack of stationarity and ergodicity. Here, we describe an unsupervised, data-driven framework to perform hypothesis testing in such situations. This consists of a statistical mechanical approach - analogous to the configuration model for networked systems - for ensembles of time series designed to preserve, on average, some of the statistical properties observed on an empirical set of time series. We showcase its possible applications with a case study on financial portfolio selection.