We investigate shrinkage priors on power spectral densities for complex-valued circular-symmetric autoregressive processes. construct predictive densities, which asymptotically dominate (i) the Bayesian density based Jeffreys prior and (ii) estimative with maximum likelihood estimator, where Kullback-Leibler divergence from true to a is adopted as risk. Furthermore, we propose general construct...

The purpose of this paper is to use Bahadur’s asymptotic relative efficiency measure to compare the performance of various tests of autoregressive (AR) versus moving average (MA) error processes in regression models. Tests to be examined include non-nested procedures of the models against each other, and classical procedures based upon testing both the AR and MA error processes against the more...

A sequence of first–order integer–valued autoregressive type (INAR(1)) processes is investigated, where the autoregressive type coefficients converge to 1. It is shown that the limiting distribution of the joint conditional least squares estimators for this coefficient and for the mean of the innovation is normal. Consequences for sequences of Galton–Watson branching processes with unobservable...

The classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. Many processes exhibit a certain degree of correlation and can be treated by autoregressive models, among which the autoregressive model of order one (AR (1))...

Univariate and multivariate empirical processes based on residuals of Infinite variance autoregressive processes are investigated. The results are used to develop tests of independence and Goodness of fit.

Previous investigation of coding sequence lengths (CDS) in the bacterial circular chromosome revealed short range correlation in the series of these data. We have further analyzed the averaged periodograms of these series and we found that the organization of CDS can be well described by first order autoregressive processes. This involves interaction between the neighboring terms. The autoregre...

We prove the large deviation principle for the posterior distributions on the (unknown) parameter of a multivariate autoregressive process with i.i.d. Normal innovations. As a particular case, we recover a previous result for univariate first-order autoregressive processes. We also show that the rate function can be expressed in terms of the divergence between two spectral densities.