We consider the effect, on a Bayes factor, of omitting observations in time-series models. In particular, we study a Bayes factor for deciding between autoregressive models of different orders. Throughout we use Gibbs sampling to estimate the parameters of the models and the marginal densities....

First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient rho = rho_n is an element of [0, 1) provided (1 - rho_n)n goes to infinity. This extends existing Gaussian limit theory by allowing for values of stationary rho...

We consider the estimation of the periods of periodic functions when their shape is unknown and they are corrupted by Gaussian white noise. In the case of a single periodic function, we propose a consistent and asymptotically efficient semiparametric estimator of the period. We then study the...

We introduce a Bayesian approach to model assessment in the class of graphical vector autoregressive processes. As a result of the very large number of model structures that may be considered, simulation-based inference, such as Markov chain Monte Carlo, is not feasible. Therefore, we derive an...

We present some new results on the mutual information between past and future for Gaussian stationary sequences. We provide several formulae to calculate this quantity. As a by-product, we establish the so-called reflectrum identity that links partial autocorrelation coefficients and cepstrum...

Several models have been proposed in recent years for analysing spatial data and also, to some extent, spatio-temporal data. One of the important problems, namely the choice of an appropriate model for describing real data sets, remains unsolved. Here we consider the analysis of spatio-temporal...

We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible autoregressive moving-average (ARMA) time series models, which were initially established by Hannan [Journal of Applied Probability (1973) vol. 10, pp. 130-145]...

An integer-valued analogue of the classical generalized autoregressive conditional heteroskedastic (GARCH) (p,q) model with Poisson deviates is proposed and a condition for the existence of such a process is given. For the case p = 1, q = 1, it is explicitly shown that an integer-valued GARCH...

A scalar pth-order autoregression (AR(p)) is considered with heteroskedasticity of the unknown form delivered by a transition function of time. A limit theory is developed and three heteroskedasticity-robust test statistics are proposed for inference, one of which is based on the nonparametric...