## Sónia Gouveia

## Autocorrelation impact on the discrepancy between IND and geometric distributions

The probability distribution of inter-nucleotide distances (IND) deviates significantly from the expected distribution obtained assuming independent random placement (i.e., the geometric distribution). The deviations can be used to discriminate among species and to build phylogenetic trees. This work investigates the extent to which DNA autocorrelation structure explains this discrepancy by considering a binary autoregressive (BinAR) model associated with the 0/1 indicator sequence of each nucleotide (A,C,G,T).

Maria Eduarda Silva

## Multivariate models for integer-valued time series

Time series of counts are available in a wide variety of fields and the need to analyse such data adequately led to a multiplicity of approaches and a diversification of models that explicitly account for the discreteness of the data. One such approach consists in replacing the multiplication in the

conventional ARMA models by an appropriate random operator, denominated thinning operator, originating the so called INARMA models. In the context of univariate time series of counts, the class of INARMA models has been widely studied in the literature. However, for multivariate time series of counts several difficulties arise and the literature is not so elaborate. In this work we address the problem of modelling multivariate time series of counts. Models based on thinning operations for bivariate time series of counts are introduced and their statistical and probabilistic properties discussed. The models and methods are illustrated in simulated and real data sets.

conventional ARMA models by an appropriate random operator, denominated thinning operator, originating the so called INARMA models. In the context of univariate time series of counts, the class of INARMA models has been widely studied in the literature. However, for multivariate time series of counts several difficulties arise and the literature is not so elaborate. In this work we address the problem of modelling multivariate time series of counts. Models based on thinning operations for bivariate time series of counts are introduced and their statistical and probabilistic properties discussed. The models and methods are illustrated in simulated and real data sets.