Random coefficient autoregressive processes describe Brownian yet non-Gaussian diffusion in heterogeneous systems

Gaussian Processes for Functional-Coefficient Autoregressive Models

This work is concerned with nonlinear time series models and, in particular, with nonparametric models for the dynamics of the mean of the time series. We build on the functional-coefficient autoregressive (FAR) model of Chen and Tsay (1993) which is a generalization of the autoregressive (AR) model where the coefficients are varying and are given by functions of the lagged values of the series...

Autoregressive Gaussian Random Vectors of First Order

Parameter estimation for non-Gaussian autoregressive processes

It is proposed to jointly estimate the parameters of nonGaussian autoregressive (AR) processes in a Bayesian context using the Gibbs sampler. Using the Markov chains produced by the sampler an approximation to the vector MAP estimator is implemented. The results reported here used AR(4) models driven by noise sequences where each sample is iid as a two component Gaussian sum mixture. The result...

Nonminimum phase non-Gaussian autoregressive processes.

The structure of non-Gaussian autoregressive schemes is described. Asymptotically efficient methods for the estimation of the coefficients of the models are described under appropriate conditions, some of which relate to smoothness and positivity of the density function f of the independent random variables generating the process. The principal interest is in nonminimum phase models.

Brownian yet Non-Gaussian Diffusion: From Superstatistics to Subordination of Diffusing Diffusivities

Aleksei V. Chechkin, Flavio Seno, Ralf Metzler, and Igor M. Sokolov Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany INFN, Padova Section, and Department of Physics and Astronomy “G. Galilei,” University of Padova, Via Marzolo 8 35131 Padova, Italy Akhiezer Institute for Theoretical Physics, Kharkov 61108, Ukraine Institute of Physics, Humboldt University Be...