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In many applications, it is of interest to study trends over time in relationships among categorical variables, such as age group, ethnicity, religious affiliation, political party and preference for particular policies. At each time point,…

An important task in data analysis is the discovery of causal relationships between observed variables. For continuous-valued data, linear acyclic causal models are commonly used to model the data-generating process, and the inference of…

This paper proposes a framework for adaptively learning a feedback linearization-based tracking controller for an unknown system using discrete-time model-free policy-gradient parameter update rules. The primary advantage of the scheme over…

The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically,…

Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…

We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…

Real-world data often exhibits sequential dependence, across diverse domains such as human behavior, medicine, finance, and climate modeling. Probabilistic methods capture the inherent uncertainty associated with prediction in these…

We present a method for the joint analysis of a panel of possibly nonstationary time series. The approach is Bayesian and uses a covariate-dependent infinite mixture model to incorporate multiple time series, with mixture components…

Causal inference from observational data following the restricted structural causal model (SCM) framework hinges largely on the asymmetry between cause and effect from the data generating mechanisms, such as non-Gaussianity or nonlinearity.…

This paper proposes a regression tree procedure to estimate conditional copulas. The associated algorithm determines classes of observations based on covariate values and fits a simple parametric copula model on each class. The association…

This article introduces autocorrelograms for time series of point processes. Such time series usually arise when a longer temporal or spatio-temporal point process is sliced into smaller time units; for example, when an annual process is…

In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and…

We study ergodic properties of some Markov chains models in random environments when the random Markov kernels that define the dynamic satisfy some usual drift and small set conditions but with random coefficients. In particular, we adapt a…

We formulate and analyze a graphical model selection method for inferring the conditional independence graph of a high-dimensional nonstationary Gaussian random process (time series) from a finite-length observation. The observed process…

In many scenarios, it is necessary to monitor a complex system via a time-series of observations and determine when anomalous exogenous events have occurred so that relevant actions can be taken. Determining whether current observations are…

We propose a framework for determining whether the causal dependence of an outcome $Y$ on a covariate $X$ changes at a given time point, given confounders $\boldsymbol{Z}$. For instance, in financial markets, the effect of a market…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

In this paper, we adopt results in nonlinear time series analysis for causal inference in dynamical settings.~Our motivation is policy analysis with panel data, particularly through the use of "synthetic control" methods. These methods…

In many time-to-event studies, the event of interest is recurrent. Here, the data for each sample unit corresponds to a series of gap times between the subsequent events. Given a limited follow-up period, the last gap time might be…

This paper incorporates information about the temporal order of regressors to estimate orthogonal and economically interpretable regression coefficients. We establish new finite sample properties for the Gram-Schmidt orthogonalization…