Esmeralda Gonçalves

Epidemiology of autism spectrum disorder in Portugal: prevalence, clinical characterization, and medical conditions

The objective of this study was to estimate the prevalence of autistic spectrum disorder (ASD) and identify its clinical characterization, and medical conditions in a paediatric population in Portugal. A school survey was conducted in elementary schools, targeting 332 808 school‐aged children in the mainland and 10 910 in the Azores islands. Referred children were directly assessed using the Diagnostic and Statistical Manual of Mental Disorders (4th edn), the Autism Diagnostic Interview–Revised, and the Childhood Autism Rating Scale. Clinical history and a laboratory investigation was performed. In parallel, a systematic multi‐source search of children known to have autism was carried out in a restricted region. The global prevalence of ASD per 10 000 was 9.2 in mainland, and 15.6 in the Azores, with intriguing regional differences. A diversity of associated medical conditions was documented in 20%, with an unexpectedly high rate of mitochondrial respiratory chain disorders.

Stationarity of Gtarch Processes

The study of the volatility, present in some time series, provoked the appearance of models with autoregressive conditional heteroscedasticity, called ARCH (ENGLE (1982)). In order to account for asymmetries in the volatility, RABEMANANJARA & ZAKOIAN (1992) introduced a new formulation for the conditional variance expressing it as a piecewise linear function of past values of the process as well as of past values of the conditional variance itself. The aim of this paper is to study the strong stationarity and the ergodicity of this kind of models, called GTARCH. As a consequence, we obtain, for some concrete models, regions of stationarity for thier coefficients.

A Decision Procedure for Bilinear Time Series Based on the Asymptotic Separation

This paper presents a non-classical decision procedure for a bilinear model with a general error process. This procedure allows us to decide, in a consistent way, between two hypotheses on the model. By establishing the asymptotic separation of the sequences of probability laws defined by each hypothesis, we obtain the consistence of this decision method. Some studies about the rate of convergence are presented and an exponential decay is obtained. A simulation study is done to illustrate the behaviour of the power and level functions in small and moderate samples when this procedure is used as a test.

Zero-inflated compound Poisson distributions in integer-valued GARCH models

In this paper we introduce a wide class of integer-valued stochastic processes that allows to take into consideration, simultaneously, relevant characteristics observed in count data namely zero inflation, overdispersion and conditional heteroscedasticity. This class includes, in particular, the compound Poisson, the zero-inflated Poisson and the zero-inflated negative binomial INGARCH models, recently proposed in literature. The main probabilistic analysis of this class of processes is here developed. Precisely, first- and second-order stationarity conditions are derived, the autocorrelation function is deduced and the strict stationarity is established in a large subclass. We also analyse in a particular model the existence of higher-order moments and deduce the explicit form for the first four cumulants, as well as its skewness and kurtosis.

Some statistical results on autoregressive conditionally heteroscedastic models

Abstract The aim of this paper is to present some statistical aspects of an order 1 autoregressive model with errors following a stationary and ergodic generalized threshold ARCH process. So, to analyse the precision of forecasts obtained with these models a probabilistic study will be done. Moreover, a consistent test for a general AR(1) model with errors following an ergodic white noise of null conditional median will be developed and adapted to our stochastic process.

A new test for ARMA models with errors following a general white noise process

SummaryThe aim of this paper is to present a new test for ARMA models. The consistency of this sequence of tests is proved using the asymptotic separation of the two sequences of probability laws defined by each hypothesis to be tested. Furthermore, we illustrate the adequacy of this test for general ARMA models in which the error process is conditionally heteroscedastic white noise. Therefore, beyond its application to classical ARMA processes, this test is also well-adapted to ARMA-GARCH and ARMA-GTARCH models.

On the Finite Dimensional Laws of Threshold GARCH Processes

In this chapter we establish bounds for the finite dimensional laws of a threshold GARCH process, X, with generating process Z. In this class of models the conditional standard deviation has different reactions according to the sign of past values of the process. So, we firstly find lower and upper bounds for the law of \(\left ({X}_{1}^{+},-{X}_{1}^{+},\ldots,{X}_{n}^{+},-{X}_{n}^{+}\right )\), in certain regions of \({\mathbb{R}}^{2n}\), and use them to find bounds of the law of \(\left ({X}_{1},\ldots,{X}_{n}\right )\). Some of these bounds only depend on the parameters of the model and on the distribution function of the independent generating process, Z. An application of these bounds to control charts for time series is presented.

Zero-truncated compound Poisson integer-valued GARCH models for time series

ABSTRACT Starting from the compound Poisson INGARCH models, we introduce in this paper a new family of integer-valued models suitable to describe count data without zeros that we name zero-truncated CP-INGARCH processes. For such class of models, a probabilistic study concerning moments existence, stationarity and ergodicity is developed. The conditional quasi-maximum likelihood method is introduced to consistently estimate the parameters of a wide zero-truncated compound Poisson subclass of models. The conditional maximum likelihood method is also used to estimate the parameters of ZTCP-INGARCH processes associated with well-specified conditional laws. A simulation study that compares some of those estimators and illustrates their finite distance behaviour as well as a real-data application conclude the paper.

On the Distribution Estimation of Power Threshold Garch Processes

The aim of this paper is to estimate the probability distribution of power TGARCH processes by establishing bounds for their nite dimensional laws. These bounds only depend on the parameters of the model and on the distribu- tion function of its independent generating process. The application of this study to some particular models allows us to conjecture that this procedure is an ade- quate alternative to the corresponding estimation using the empirical distribution functions, particularly useful in the development of control charts for this kind of models.