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.

We propose an integer-valued stochastic process with conditional marginal distribution belonging to the class of infinitely divisible discrete probability laws. With this proposal, we introduce a wide class of models for count time series that includes the Poisson integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) model (Ferland et al., 2006) and the negative binomial and generalized Poisson INGARCH models (Zhu, 2011(Zhu, , 2012a. The main probabilistic analysis of this process is developed stating, in particular, first-order and second-order stationarity conditions. The existence of a strictly stationary and ergodic solution is established in a subclass including the Poisson and generalized Poisson INGARCH models.

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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 analyze 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.

In this paper we consider the modified Shewhart control chart for ARCH processes and introduce it for threshold ARCH (TARCH) ones. For both charts, we determine bounds for the distribution of the in-control run length (RL) and, consequently, for its average (ARL), both depending only on the distribution of the generating white noise, the model parameters and the critical value. For the ARCH model, we compare our bounds with others available in literature and show how they improve the existing ones. We present a simulation study to assess the quality of the bounds calculated for the ARL.