Stationary Gaussian Markov processes as limits of stationary autoregressive time series

Stationary Gaussian Markov processes as limits of stationary autoregressive time series

Learning Stationary Time Series using Gaussian Processes with Nonparametric Kernels

We introduce the Gaussian Process Convolution Model (GPCM), a two-stage nonparametric generative procedure to model stationary signals as the convolution between a continuous-time white-noise process and a continuous-time linear filter drawn from Gaussian process. The GPCM is a continuous-time nonparametricwindow moving average process and, conditionally, is itself a Gaussian process with a non...

The Generation of Stationary Gaussian Time Series

Three di erent algorithms for the generation of stationary Gaussian time series with given autocorrelation function are presented in this paper. The algorithms have already been suggested in the literature but are not well known and have never been compared before. Interrelations between the di erent methods, advantages and disadvantages with respect to speed and memory requirements and the ran...

Stationary space-time Gaussian fields and their time autoregressive representation

We compare two different modelling strategies for continuous space discrete time data. The Žrst strategy is in the spirit of Gaussian kriging. The model is a general stationary space–time Gaussian Želd where the key point is the choice of a parametric form for the covariance function. In the main, covariance functions that are used are separable in space and time. Nonseparable covariance functi...

Stationary Markov Processes

We consider some classes of stationary, counting{measure{valued Markov processes and their companions under time{reversal. Examples arise in the L evy{It^ o decomposition of stable Ornstein{Uhlenbeck processes, the large{time asymptotics of the standard additive coalescent, and extreme value theory. These processes share the common feature that points in the support of the evolving counting{ me...