Binary versus non-binary information in real time series: empirical results and maximum-entropy matrix models

Abstract

The dynamics of complex systems, from financial markets to the brain, can be monitored in terms of multiple time series of activity of the constituent units, such as stocks or neurons respectively. While the main focus of time series analysis is on the magnitude of temporal increments, a significant piece of information is encoded into the binary projection (i.e. the sign) of such increments. In this paper we provide further evidence of this by showing strong nonlinear relations between binary and non-binary properties of financial time series. These relations are a novel quantification of the fact that extreme price increments occur more often when most stocks move in the same direction. We then introduce an information-theoretic approach to the analysis of the binary signature of single and multiple time series. Through the definition of maximum-entropy ensembles of binary matrices and their mapping to spin models in statistical physics, we quantify the information encoded into the simplest binary properties of real time series and identify the most informative property given a set of measurements. Our formalism is able to accurately replicate, and mathematically characterize, the observed binary/non-binary relations. We also obtain a phase diagram allowing us to identify, based only on the instantaneous aggregate return of a set of multiple time series, a regime where the so-called `market mode' has an optimal interpretation in terms of collective (endogenous) effects, a regime where it is parsimoniously explained by pure noise, and a regime where it can be regarded as a combination of endogenous and exogenous factors. Our approach allows us to connect spin models, simple stochastic processes, and ensembles of time series inferred from partial information.

References in corpus (17)

• Hierarchical Structure in Financial Markets
• Weak pairwise correlations imply strongly correlated network states in a neural population
• Noise Dressing of Financial Correlation Matrices
• Universal and non-universal properties of cross-correlations in financial time series
• A Random Matrix Approach to Cross-Correlations in Financial Data
• The statistical mechanics of networks
• The leverage effect in financial markets: retarded volatility and market panic
• Dynamic asset trees and Black Monday
• Analytical maximum-likelihood method to detect patterns in real networks
• Maximum likelihood: extracting unbiased information from complex networks
• Volatility clustering and scaling for financial time series due to attractor bubbling
• Generalized percolation in random directed networks
• Randomizing world trade. I. A binary network analysis
• Randomizing world trade. II. A weighted network analysis
• Quantitative law describing market dynamics before and after interest-rate change
• Multiplicative point process as a model of trading activity
• The non-random walk of stock prices: The long-term correlation between signs and sizes

Cited by in corpus (4)

• Mesoscopic Community Structure of Financial Markets Revealed by Price and Sign Fluctuations
• Strong ensemble nonequivalence in systems with local constraints
• Maximum Entropy approach to multivariate time series randomization
• Nonparametric sign prediction of high-dimensional correlation matrix coefficients