Taiane Schaedler Prass

Here we present a theoretical study on the main properties of Fractionally Integrated Exponential Generalized Autoregressive Conditional Heteroskedastic (FIEGARCH) processes. We analyze the conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We prove that, if {Xt}t∈Z is a FIEGARCH(p,d,q) process then, under mild conditions, {ln(Xt2)}t∈Z is an ARFIMA(q,d,0) with correlated innovations, that is, an autoregressive fractionally integrated moving average process. The convergence order for the polynomial coefficients that describes the volatility is presented and results related to the spectral representation and to the covariance structure of both processes {ln(Xt2)}t∈Z and {ln(σt2)}t∈Z are discussed. Expressions for the kurtosis and the asymmetry measures for any stationary FIEGARCH(p,d,q) process are also derived. The h-step ahead forecast for the processes {Xt}t∈Z, {ln(σt2)}t∈Z and {ln(Xt2)}t∈Z are given with their respective mean square error of forecast. The work also presents a Monte Carlo simulation study showing how to generate, estimate and forecast based on six different FIEGARCH models. The forecasting performance of six models belonging to the class of autoregressive conditional heteroskedastic models (namely, ARCH-type models) and radial basis models is compared through an empirical application to Brazilian stock market exchange index.

Here we develop the theory of seasonal FIEGARCH processes, denoted by SFIEGARCH, establishing conditions for the existence, the invertibility, the stationarity and the ergodicity of these processes. We analyze their asymptotic dependence structure by means of the autocovariance and autocorrelation functions. We also present some properties regarding their spectral representation. All properties are illustrated through graphical examples and an application of SFIEGARCH models to describe the volatility of the S&P500 US stock index log-return time series in the period from December 13, 2004 to October 10, 2009 is provided.

Objective: Vaccines are effective in controlling and eradicating infectious diseases. However, adverse events following immunization (AEFI) can occur in susceptible individuals. The objective of this study was to analyze the Brazilian AEFI database and compare eight vaccines in order to profile risks of AEFIs related to the mandated pediatric schedule of immunization, considering the age and sex of the child, type of vaccine, and reported adverse events. Methods: We analyzed the Brazilian AEFI database integrating reports between 2005 and 2010 for children less than 10-years old immunized with eight mandated vaccines: diphtheria, pertussis, tetanus, Haemophilus influenzae type b (TETRA); diphtheria, tetanus, and pertussis (DTP); Bacillus Calmette–Guerin (BCG); oral poliovirus vaccine (OPV); measles, mumps, and rubella (MMR); oral rotavirus vaccine (ORV); hepatitis B (HB); and yellow fever (YF). We compared the children’s age regarding types of AEFI, evaluated AEFI factors associated with the chance of hospitalization of the child, and estimated the chance of notification of an AEFI as a function of the type of vaccine. In total, 47,105 AEFIs were observed for the mandated vaccines. Results: The highest AEFI rate was for the TETRA vaccine and the lowest was for the OPV vaccine, with 60.1 and 2.3 events per 100,000 inoculations, respectively. The TETRA vaccine showed the highest rate of hypotonic hyporesponsive episode, followed by convulsion and fever. The MMR and YF vaccines were associated with generalized rash. BCG was associated with enlarged lymph glands but showed the largest negative (protective) association with hyporesponsive events and seizures. Compared with children aged 5–9-years old, young children (<1 year) showed significantly higher odds of hospitalization. Conclusions: The Brazilian AEFI registry is useful to compare the magnitude and certain characteristics of adverse events associated with mandated pediatric vaccines.