Latent Gaussian Count Time Series Modeling

This paper develops theory and methods for the copula modeling of stationary count time series. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very flexible correlation features that can have any pre-specified marginal distribution, including the classical Poisson, generalized Poisson, negative binomial, and binomial count structures. A Gaussian pseudo-likelihood estimation paradigm, based only on the mean and autocovariance function of the count series, is developed via some new Hermite expansions. Particle filtering methods are studied to approximate the true likelihood of the count series. Here, connections to hidden Markov models and other copula likelihood approximations are made. The efficacy of the approach is demonstrated and the methods are used to analyze a count series containing the annual number of no-hitter baseball games pitched in major league baseball since 1893

Integrable Floquet dynamics, generalized exclusion processes and "fused" matrix ansatz

We present a general method for constructing integrable stochastic processes, with two-step discrete time Floquet dynamics, from the transfer matrix formalism. The models can be interpreted as a discrete time parallel update. The method can be applied for both periodic and open boundary conditions. We also show how the stationary distribution can be built as a matrix product state. As an illustration we construct a parallel discrete time dynamics associated with the R-matrix of the SSEP and of the ASEP, and provide the associated stationary distributions in a matrix product form. We use this general framework to introduce new integrable generalized exclusion processes, where a fixed number of particles is allowed on each lattice site in opposition to the (single particle) exclusion process models. They are constructed using the fusion procedure of R-matrices (and K-matrices for open boundary conditions) for the SSEP and ASEP. We develop a new method, that we named "fused" matrix ansatz, to build explicitly the stationary distribution in a matrix product form. We use this algebraic structure to compute physical observables such as the correlation functions and the mean particle current.Comment: 33 pages, to appear in Nuclear Physics