We consider the estimation of the multivariate regression function m (x 1 , . . . ,xd) = E [ψ (Yd) | X 1 = x 1 , . . . ,Xd = xd], and its partial derivatives, for stationary random processes {Yi ,Xi} using local higher-order polynomial fitting. Particular cases of ψ yield estimation of the conditional mean, conditional moments and conditional distributions. Joint asymptotic normality is establi...

Classical spectral analysis in statistics considers decomposition of stationary time series into sinusoidal components. The autocovariance and the spectrum are fundamental elements for analyzing a given time series both in time and frequency domain. However, in practice one frequently observes nonstationary time series. In order to apply spectral analysis to these processes, an extension of the...

We describe and illustrate Bayesian approaches to modelling and analysis of multiple non-stationary time series. This begins with univariate models for collections of related time series assumedly driven by underlying but unobservable processes, referred to as dynamic latent factor processes. We focus on models in which the factor processes, and hence the observed time series, are modelled by t...

We describe and illustrate Bayesian approaches to modelling and analysis of multiple non-stationary time series. This begins with uni-variate models for collections of related time series assumedly driven by underlying but unobservable processes, referred to as dynamic latent factor processes. We focus on models in which the factor processes, and hence the observed time series, are modelled by ...

We employ an ergodic theory argument to demonstrate the foundations of ubiquity of Lévy stable self-similar processes in physics and present a class of models for anomalous and nonextensive diffusion. A relationship between stationary and self-similar models is clarified. The presented stochastic integral description of all Lévy stable processes could provide new insights into the mechanism und...

A tempered stable Lévy process combines both the α–stable and Gaussian trends. In a short time frame it is close to an α–stable process while in a long time frame it approximates a Brownian motion. In this paper we consider a general and robust class of multivariate tempered stable distributions and establish their identifiable parametrization. We prove short and long time behavior of tempered ...