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...

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...

In this paper the author considers an autoregressive process where the parameters of the process are unknown and try to obtain pivots for predicting future observations. If we do a probabilistic prediction with the estimated model, where the parameters are estimated by a sample of size n, we introduce an error of order n−1 in the coverage probabilities of the prediction intervals. However we ca...

We consider the problem of choosing the optimal (in the sense of mean-squared prediction error) multistep predictor for an autoregres-sive (AR) process of finite but unknown order. If a working AR model (which is possibly misspecified) is adopted for multistep predictions, then two competing types of multistep predictors (i.e., plug-in and direct predictors) can be obtained from this model. We ...

We consider the sets of moving-average and autoregressive processes and study their closures under the Mallows metric and the total variation convergence on nite dimensional distributions. These closures are unexpectedly large, containing nonergodic processes which are Poisson sums of i.i.d. copies from a stationary process. The presence of these non-ergodic Poisson sum processes has immediate ...

We consider model identification for infinite variance autoregressive time series processes. It is shown that a consistent estimate of autoregressive model order can be obtained by minimizing Akaike’s information criterion, and we use all-pass models to identify noncausal autoregressive processes and estimate the order of noncausality (the number of roots of the autoregressive polynomial inside...

Riassunto: L’obiettivo del presente lavoro è studiare il comportamento di una nuova procedura per la determinazione di regioni di previsione per processi autoregressivi multidimensionali. Le regioni di previsione, basate sulla tecnica bootstrap, non fanno affidamento su alcuna assunzione distributiva per i disturbi ed inoltre tengono conto della variabilità derivante dalla necessità di stimare ...

A method is shown for computing transfer entropy over multiple time lags for coupled autoregressive processes using formulas for the differential entropy of multivariate Gaussian processes. Two examples are provided: (1) a first-order filtered noise process whose state is measured with additive noise, and (2) two first-order coupled processes each of which is driven by white process noise. We f...

We consider the problem of fitting a Gaussian autoregressive model to a time series, subject to conditional independence constraints. This is an extension of the classical covariance selection problem to times series. The conditional independence constraints impose a sparsity pattern on the inverse of the spectral density matrix, and result in nonconvex quadratic equality constraints in the max...