Maximum entropy approach to multivariate time series randomization

Riccardo Marcaccioli,Giacomo Livan

doi:10.1038/s41598-020-67536-y

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.

Highlights

Natural and social multivariate systems are commonly studied through sets of simultaneous and timespaced measurements of the observables that drive their dynamics, i.e., through sets of time series
In its general formulation, it hinges upon contrasting the observed statistical properties of a system with those expected under a null hypothesis
This, in turn, makes hypothesis testing in complex systems a very challenging task, that potentially prevents from assessing which properties observed in a given data sample are “untypical”, i.e, unlikely to be observed again in a sample collected at a different point in time

Summary

Introduction

Natural and social multivariate systems are commonly studied through sets of simultaneous and timespaced measurements of the observables that drive their dynamics, i.e., through sets of time series 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, in turn, makes hypothesis testing in complex systems a very challenging task, that potentially prevents from assessing which properties observed in a given data sample are “untypical”, i.e, unlikely to be observed again in a sample collected at a different point in time This issue is usually tackled by constructing ensembles of artificial time series sharing some characteristics with those generated by the dynamics of the system under study. Once calibrated, autoregressive models produce rather constrained ensembles of time series that do not allow to explore scenarios that differ substantially from those observed empirically

Objectives

Conclusion