We study the autocorrelation structure and the spectral density function of aggregates from a discrete-time process. The underlying discrete-time process is assumed to be a stationary AutoRegressive Fractionally Integrated Moving-Average (ARFIMA) process, after suitable number of differencing if...

This paper addresses the problem of identifying echelon canonical forms for a vector autoregressive moving-average model with exogenous variables using finite algorithms. For given values of the Kronecker indices, a method for estimating the structural parameters of a model using ordinary least...

The rank of the spectral density matrix conveys relevant information in a variety of statistical modelling scenarios. This note shows how to estimate the rank of the spectral density matrix at any given frequency. The method presented is valid for any hermitian positive definite matrix estimate...

The paper presents a central limit theorem and an allied invariance theorem related to what Marinucci and Robinson [Journal of Statistics, Planning and Inference (1999) Vol. 21, pp. 111-122] termed type II fractional Brownian motion. To widen the applicability, their independent and identically...

The innovations algorithm can be used to obtain parameter estimates for periodically stationary time series models. In this paper, we compute the asymptotic distribution for these estimates in the case, where the innovations have a finite fourth moment. These asymptotic results are useful to...

We consider robust serial correlation tests in autoregressive models with exogenous variables (ARX). Since the least squares estimators are not robust when outliers are present, a new family of estimators is introduced, called residual autocovariances for ARX (RA-ARX). They provide resistant...

We study the problem of model selection with nuisance parameters present only under the alternative. The common approach for testing in this case is to determine the true model through the use of some functionals over the nuisance parameters space. Since in such cases the distribution of these...

We consider semiparametric estimation in time-series regression in the presence of long-range dependence in both the errors and the stochastic regressors. A central limit theorem is established for a class of semiparametric frequency domain-weighted least squares estimates, which includes both...

Here we obtain difference equations for the higher order moments and cumulants of a time series {X_t} satisfying an INAR(p) model. These equations are similar to the difference equations for the higher order moments and cumulants of the bilinear time series model. We obtain the spectral and...

Parameter estimation and subset selection for separable lower triangular bilinear (SLTBL) models are considered. Under a flat prior, we present an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimation. Furthermore, two sub-procedures are designed to select the best...