21,093 research outputs found
A Robust Class of Linear Recurrence Sequences
We introduce a subclass of linear recurrence sequences which we call poly-rational sequences because they are denoted by rational expressions closed under sum and product. We show that this class is robust by giving several characterisations: polynomially ambiguous weighted automata, copyless cost-register automata, rational formal series, and linear recurrence sequences whose eigenvalues are roots of rational numbers
A Simple Class of Bayesian Nonparametric Autoregression Models
We introduce a model for a time series of continuous outcomes, that can be expressed as fully nonparametric regression or density regression on lagged terms. The model is based on a dependent Dirichlet process prior on a family of random probability measures indexed by the lagged covariates. The approach is also extended to sequences of binary responses. We discuss implementation and applications of the models to a sequence of waiting times between eruptions of the Old Faithful Geyser, and to a dataset consisting of sequences of recurrence indicators for tumors in the bladder of several patients.MIUR 2008MK3AFZFONDECYT 1100010NIH/NCI R01CA075981Mathematic
Nonlinear time-series analysis revisited
In 1980 and 1981, two pioneering papers laid the foundation for what became
known as nonlinear time-series analysis: the analysis of observed
data---typically univariate---via dynamical systems theory. Based on the
concept of state-space reconstruction, this set of methods allows us to compute
characteristic quantities such as Lyapunov exponents and fractal dimensions, to
predict the future course of the time series, and even to reconstruct the
equations of motion in some cases. In practice, however, there are a number of
issues that restrict the power of this approach: whether the signal accurately
and thoroughly samples the dynamics, for instance, and whether it contains
noise. Moreover, the numerical algorithms that we use to instantiate these
ideas are not perfect; they involve approximations, scale parameters, and
finite-precision arithmetic, among other things. Even so, nonlinear time-series
analysis has been used to great advantage on thousands of real and synthetic
data sets from a wide variety of systems ranging from roulette wheels to lasers
to the human heart. Even in cases where the data do not meet the mathematical
or algorithmic requirements to assure full topological conjugacy, the results
of nonlinear time-series analysis can be helpful in understanding,
characterizing, and predicting dynamical systems
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