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Autoregressive and moving-average (ARMA) models with stable Paretian errors is one of the most studied models for time series with infinite variance. Estimation methods for these models have been studied by many researchers but the problem…
In a previous work, the authors proposed a Grammatical Evolution algorithm to automatically generate Lindenmayer Systems which represent fractal curves with a pre-determined fractal dimension. This paper gives strong statistical evidence…
This paper challenges the dominance of stochastic trend models by introducing the Seasonal-Trend-Stationary ARMA (STSA) framework, which represents univariate nonstationary time series as stationary fluctuations around deterministic trend…
A modified Lagrange Polynomial is introduced for polynomial extrapolation, which can be used to estimate the equally spaced values of a polynomial function. As an example of its application, this article presents a prime-generating…
The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…
We propose a nonparametric method for detecting nonlinear causal relationship within a set of multidimensional discrete time series, by using sparse additive models (SpAMs). We show that, when the input to the SpAM is a $\beta$-mixing time…
Arcade processes are a class of continuous stochastic processes that interpolate in a strong sense, i.e., omega by omega, between zeros at fixed pre-specified times. Their additive randomisation allows one to match any finite sequence of…
In this paper, we present a fractional decomposition of the probability generating function of the innovation process of the first-order non-negative integer-valued autoregressive [INAR(1)] process to obtain the corresponding probability…
Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…
The question whether a time series behaves as a random walk or as a station- ary process is an important and delicate problem, particularly arising in financial statistics, econometrics, and engineering. This paper studies the problem to…
The problem of random number generation dates back to von Neumann's work in 1951. Since then, many algorithms have been developed for generating unbiased bits from complex correlated sources as well as for generating arbitrary distributions…
We consider the problem of inference for non-stationary time series with heavy-tailed error distribution. Under a time-varying linear process framework we show that there exists a suitable local approximation by a stationary process with…
In this paper, we propose a novel variable selection approach in the framework of sparse high-dimensional GLARMA models. It consists in combining the estimation of the autoregressive moving average (ARMA) coefficients of these models with…
We consider a renewal-reward process with multivariate rewards. Such a process is constructed from an i.i.d.\ sequence of time periods, to each of which there is associated a multivariate reward vector. The rewards in each time period may…
The autoregressive process of order $p$ (AR($p$)) is a central model in time series analysis. A Bayesian approach requires the user to define a prior distribution for the coefficients of the AR($p$) model. Although it is easy to write down…
A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of…
A sequential importance sampling algorithm is developed for the distribution that results when a matrix of independent, but not identically distributed, Bernoulli random variables is conditioned on a given sequence of row and column sums.…
The rate of entropy production provides a useful quantitative measure of a non-equilibrium system and estimating it directly from time-series data from experiments is highly desirable. Several approaches have been considered for stationary…
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…
We consider the problem of estimating a signal from its warped observations. Such estimation is commonly performed by altering the observations through some inverse-warping, or solving a computationally demanding optimization formulation.…