• Corpus ID: 195886221

Statistical mechanics of time series

@article{Marcaccioli2019StatisticalMO,
  title={Statistical mechanics of time series},
  author={Riccardo Marcaccioli and Giacomo Livan},
  journal={arXiv: Statistical Finance},
  year={2019}
}

• Riccardo Marcaccioli, G. Livan
• Published 1 July 2019
• Computer Science
• arXiv: Statistical Finance

Countless natural and social multivariate systems are 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 theory - derived from first principles - 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 on a set of stock market returns from the NYSE.