In this paper the integer-valued autoregressive model of order one, contaminated with additive outliers is studied in some detail. Moreover, parameter estimation is also addressed. Supposing that the timepoints of the outliers are known but their sizes are unknown, we prove that the conditional...

In this article, we prove that with probability one the k-th order upper random Stieltjes sum defined on a random sample from a distribution supported by a finite interval converges to the corresponding k-th moment distribution. When the underlying distribution is uniform U(0,θ), we prove that...

This paper investigates the asymptotic properties of the ordinary least squares (OLS) estimator of structural parameters in a stylised macroeconomic model in which agents are boundedly rational and use an adaptive learning rule to form expectations of the endogenous variable. In particular, when...

This paper provides an example of a linear regression model with predetermined stochastic regressors for which the sufficient condition for strong consistency of the ordinary least squares estimator by Lai & Wei (1982, Annals of Statistics) is not met. Nevertheless, the estimator is strongly...

In this paper, we consider the class of Markov switching bilinear processes (MS–BL) that offer remarkably rich dynamics and may be considered as an alternative to model non Gaussian data which exhibit structural changes. In these models, the parameters are allowed to depend upon a latent...

When the unobservable Markov chain in a hidden Markov model is stationary the marginal distribution of the observations is a finite mixture with the number of terms equal to the number of the states of the Markov chain. This suggests estimating the number of states of the unobservable Markov...

A vector autoregression with deterministic terms and with no restrictions to its characteristic roots is considered. Strong consistency results for the least squares statistics are presented. This extends earlier results where deterministic terms have not been considered. In addition the...

A vector autoregression with deterministic terms and with no restrictions to its characteristic roots is considered. Strong consistency results and also some weak convergence results are given for a number of least squares statistics. These statistics are related to the denominator matrix of the...