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We determine the amount of information contained in a time series of price returns at a given time scale, by using a widespread tool of the information theory, namely the Shannon entropy, applied to a symbolic representation of this time…
The nature of neural codes is central to neuroscience. Do neurons encode information through relatively slow changes in the emission rates of individual spikes (rate code), or by the precise timing of every spike (temporal codes)? Here we…
In this work, we develop a novel framework to measure the similarity between dynamic financial networks, i.e., time-varying financial networks. Particularly, we explore whether the proposed similarity measure can be employed to understand…
Intrinsic time is an example of an event-based conception of time, used to analyze financial time series. Here, for the first time, we reveal the connection between intrinsic time and physical time. In detail, we present an analytic…
Intrinsic computation refers to how dynamical systems store, structure, and transform historical and spatial information. By graphing a measure of structural complexity against a measure of randomness, complexity-entropy diagrams display…
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter…
We propose a new estimator to measure directed dependencies in time series. The dimensionality of data is first reduced using a new non-uniform embedding technique, where the variables are ranked according to a weighted sum of the amount of…
As experiments advance to record from tens of thousands of neurons, statistical physics provides a framework for understanding how collective activity emerges from networks of fine-scale correlations. While modeling these populations is…
Identification of latent binary sequences from a pool of noisy observations has a wide range of applications in both statistical learning and population genetics. Each observed sequence is the result of passing one of the latent…
An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…
Biological information processing networks consist of many components, which are coupled by an even larger number of complex multivariate interactions. However, analyses of data sets from fields as diverse as neuroscience, molecular…
Using results from neurobiology on perceptual decision making and value-based decision making, the problem of decision making between lotteries is reformulated in an abstract space where uncertain prospects are mapped to corresponding…
This paper presents a statistical parser for natural language that obtains a parsing accuracy---roughly 87% precision and 86% recall---which surpasses the best previously published results on the Wall St. Journal domain. The parser itself…
Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…
The price of financial assets are, since Bachelier, considered to be described by a (discrete or continuous) time sequence of random variables, i.e a stochastic process. Sharp scaling exponents or unifractal behavior of such processes has…
Recent years have seen a resurgence in interest in marketing mix models (MMMs), which are aggregate-level models of marketing effectiveness. Often these models incorporate nonlinear effects, and either implicitly or explicitly assume that…
The constituents of a complex system exchange information to function properly. Their signalling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange…
A time series is uniquely represented by its geometric shape, which also carries information. A time series can be modelled as the trajectory of a particle moving in a force field with one degree of freedom. The force acting on the particle…
In this paper, we derive and analyze a continuous of a binary option market with exogenous information. The resulting non-linear system has a discontinuous right hand side, which can be analyzed using zero-dimensional Filippov surfaces.…
Time series forecasting is widely used in a multitude of domains. In this paper, we present four models to predict the stock price using the SPX index as input time series data. The martingale and ordinary linear models require the…