Replicated INAR(1) processes

Replicated time series are a particular type of repeated measures, which consist of time-sequences of measurements taken from several subjects (experimental units). We consider independent replications of count time series that are modelled by first-order integer-valued autoregressive processes, INAR(1). In this work, we propose several estimation methods using the classical and the Bayesian approaches and both in time and frequency domains. Furthermore, we study the asymptotic properties of the estimators. The methods are illustrated and their performance is compared in a simulation study. Finally, the methods are applied to a set of observations concerning sunspot data.PRODEP II

On the Graded Identities for Elementary Gradings in Matrix Algebras over Infinite Fields

We find a basis for the $G$-graded identities of the $n\times n$ matrix algebra $M_n(K)$ over an infinite field $K$ of characteristic $p>0$ with an elementary grading such that the neutral component corresponds to the diagonal of $M_n(K)$

Estimating stellar rotation from starspot detection during planetary transits

A new method for determining the stellar rotation period is proposed here, based on the detection of starspots during transits of an extra-solar planet orbiting its host star. As the planet eclipses the star, it may pass in front of a starspot which will then make itself known through small flux variations in the transit light curve. If we are lucky enough to catch the same spot on two consecutive transits, it is possible to estimate the stellar rotational period. This method is successfully tested on transit simulations on the Sun yielding the correct value for the solar period. By detecting two starspots on more than one transit of HD 209458 observed by the Hubble Space Telescope, it was possible to estimate a period of either 9.9 or 11.4 days for the star, depending on which spot is responsible for the signature in the light curve a few transits later. Comparison with period estimates of HD209458 reported in the literature indicates that 11.4 days is the most likely stellar rotation period.Comment: 13 pages, 5 figure

Estimation and forecasting in SUINAR(1) model

This work considers a generalization of the INAR(1) model to the panel data first order Seemingly Unrelated INteger AutoRegressive Poisson model, SUINAR(1). It presents Bayesian and classical methodologies to estimate the parameters of Poisson SUINAR(1) model and to forecast future observations of the process. In particular, prediction intervals for forecasts - classical approach - and HPD prediction intervals - Bayesian approach - are derived. A simulation study is provided to give additional insight into the finite sample behaviour of the parameter estimates and forecasts