Modeling count data through INAR models

Modeling count data through INAR models

Time series of counts are present in different fields of science and the need to analyze these data adequately led to the development of several approaches that take into account the discrete nature of the data. One way of doing this is through the INARMA models, which are based on an appropriate random operator and the most commonly used one is the binomial thinning operator.
While the analysis and application of univariate INAR models is a subject extensively studied in the literature, multivariate models are still in development and the literature on this topic is much more reduced.
In this work we bring forward the problem of modeling univariate and bivariate time series of counts using INAR models. The models and methods are illustrated through simulated data and real data sets.

Magda Monteiro
ESTGA - Universidade de Aveiro
CIDMA - Centro de Investigação e Desenvolvimento em Matemática e Aplicações

Categorization of continuous variables in clinical prediction models. Development, validation and application of a new approach.

Categorization of continuous variables in clinical prediction models. Development, validation and application of a new approach.

In the development of clinical prediction models it is common to use categorical variables as predictors, especially when those models aim to be applied in daily clinical practice as to support clinicians at decision time. The aim is to propose two methods, named AddFor and Genetic, to obtain optimal cut-points to categorize continuous predictors as to be used in clinical prediction models. The framework considered is the logistic regression model. Our proposal consists on categorizing the continuous covariate X in such a way that the best predictive logistic model is obtained (highest area under the receiver operating characteristic curve - AUC) for the response dichotomous variable Y. The proposed methods have been validated by simulation studies. Additionally, we have developed an R package, named CatPredi, which implements these methods and provides the user with the optimal cut-points and the categorized variable to be used in the prediction model. Finally, the proposed methodology has been applied to the IRYSS-COPD study.

Irantzu Barrio Beraza
Department of applied mathematics, statistics and operational research. University of the Basque Country UPV/EHU. Spain

Sectoral labor market flexibility in a small open economy

Sectoral labor market flexibility in a small open economy

We compute an index of sectoral labor market flexibility and use it to estimate the effect of exchange rate movements on employment in Portugal. Our sectoral index indicates that manufacturing labor markets have become more flexible in recent years, albeit at a different pace from what the OECD's EPL index suggests. Furthermore, our index shows that there is heterogeneity at the sector level. Our econometric application indicates that our measure of sectoral labor market flexibility, alongside the level of technology and trade openness, is relevant for understanding the reaction of employment to movements in exchange rates.

Keywords: employment, exchanges rates, international trade, labor market flexibility, technology.

Miguel Portela
Miguel Portela (NIPE/EEG - U. Minho)
Fernando Alexandre (EEG - University of Minho), Pedro Bação (FE - University of Coimbra and GEMF), João Cerejeira (EEG - University of Minho and NIPE).

Modeling Spatial Extremes: an application to monthly extreme precipitation

Modeling Spatial Extremes: an application to monthly extreme precipitation

Spatial statistics deals with statistical methods in which spatial locations play an explicit role. Natural hazards such as high rainfall and windstorms arise due to physical processes and are spatial in extent. Classical geostatistics, mostly based on multivariate normal distributions, is then inappropriate for modeling tail behavior. Spatial extreme analysis joins two areas of statistics: extreme value analysis and geostatistics. Several statistical procedures have been proposed for spatial modeling of extremes based on Bayesian hierarchical models, copulas and max-stable processes. Max-stable processes form a natural class of processes extending extreme value theory when sample maxima are observed at each site of a spatial process. Recent developments of extremal spatial approaches are here reviewed. A real case of extreme spatial precipitation in Portugal is discussed.
Acknowledgments: Research partially supported by National Funds through FCT, projects PEst-OE/MAT/UI0006/2011 (CEAUL), PEst-OE/MAT/UI0297/2011 (CMA/UNL) and EXTREMA, PTDC/MAT/101736/2008.

Dora Prata Gomes
(FCT/CMA, Universidade Nova de Lisboa)

Finite mixture models and extensions

Finite mixture models and extensions

The identification of groups or clusters in data sets has become an important topic of research. Sciences like biology, medicine, social sciences, economics, or management sciences face research questions that somehow have to do with clustering. From market segmentation to the identification of groups of patients with different patterns of health needs, researchers aim to identify homogeneous groups. In contrast to heuristic-based rules of clustering, model-based clustering takes a probabilistic nature given by a mixture of probability distributions. This paper discusses finite mixture models and extensions to longitudinal data. Several examples illustrate distinct specifications of the mixture model. A case study using returns from European stock markets fully apply a dynamic mixture model to time series data.

José G. Dias
BRU/ISCTE - I.U. Lisboa

Estimation of the extremal temporal dependence in river floods

Estimation of the extremal temporal dependence in river floods

Ramos and Ledford (2009) constructed a flexible parametric joint tail model that accommodates asymptotic dependence, asymptotic independence and asymmetry within a single straightforward parsimonious parameterisation. Using this parametric model, we analyse short-range temporal dependence within stationary time series, characterising the extremal behaviour of the series. Recently, to characterise the extremal behaviour of a stationary time series, attention has been given to the within-cluster behaviour of the extremes of a series, which is determined by the short-range temporal dependence. Most of its characterization has been done based on the assumption of Markovianity of the time series, as the class of dth-order Markov chains is sufficiently general and tractable. We consider here joint tails of the distribution of two consecutive pairs (Xi;Xi+1) of a first-order stationary Markov chain being modelled by the joint tail model described in Ramos and Ledford (2009). Applying this modelling approach to hydrological data, we examine successive flood peaks, which requires the joint estimation of the extremal temporal dependence structure as well as the tail of the marginal distribution. In particular, we are interested in studying the strength of extremal dependence in the upper joint tail and the heaviness of the tails.

Alexandra Ramos
(FE/CMUP - U. Porto)