This paper deals with the estimation of seasonal long-memory time series models in the presence of 'outliers'. It is long known that the presence of outliers can lead to undesirable effects on the statistical estimation methods, for example, substantially impacting the sample autocorrelations. Thus, the aim of this work is to propose a semiparametric robust estimator for the fractional parameters in the seasonal autoregressive fractionally integrated moving average (SARFIMA) model, through the use of a robust periodogram at both very low and seasonal frequencies. The model and some theories related to the estimation method are discussed. It is shown by simulations that the robust methodology behaves like the classical one to estimate the long-memory parameters if there are no outliers (no contamination). On the other hand, in the contaminated scenario (presence of outliers), the standard methodology leads to misleading results while the proposed method is unaffected. The methodology is applied to model and forecast

Since the first official case of COVID-19 was reported, many researchers around the world have spent their time trying to understand the dynamics of the virus by modeling and predicting the number of infected and deaths. The rapid spread and highly contagiousness motivate the necessity of monitoring cases in real-time, aiming to keep control of the epidemic. As pointed out by [3] , some pitfalls like limited infrastructure, laboratory confirmation and logistical problems may cause reporting delay, leading to distortions of the real dynamics of the confirmed cases and deaths. The aim of this study is to propose a suitable statistical methodology for modeling and forecasting daily deaths and reported cases of COVID-19, considering key features as overdispersion of data and correction of notification delay. Both, reporting delays and forecasting consider a Bayesian approach in which the daily deaths and the confirmed cases are modelled using the negative binomial (NB) distribution in order to accommodate the population heterogeneity. For the correction of notification delay, the mean number of occurrences regarding time t notified at time (mean delayed notifications) is associated to the temporal and the delay lag evolution of the notification process through a log link. With regard to daily forecasting, the functional form adopted for the number of deaths and reported cases of COVID-19 is related to the sigmoid growth equation. A variable regarding week days or days off was considered in order to account for possible reduction of the records due to the lower offer of tests on days off. To illustrate the methodology, we analyze data of deaths and infected cases of COVID-19 in Espírito Santo, Brazil. We also obtain long-term predictions.

No abstract

Recently, segmented regression has been utilized as a “working” model for a bootstrap test to detect true oxygen uptake plateau. This approach employs an iterative procedure based on least squares to fit the model. However, it is widely acknowledged that least squares is highly sensitive to outliers, often yielding inefficient estimates. This paper proposes an alternative iterative method by substituting the least squares step with a M-estimator step. Leveraging the robust features of M-estimators, the proposed method is expected to exhibit resilience against outliers. To empirically investigate the performance of the proposed method, a Monte Carlo simulation study is conducted. For comparison purposes, the classical iterative method is also considered. The results indicate that, in uncontaminated scenarios, both methods exhibit similar behavior, with the classical method presenting a slightly superior performance. However, in contaminated cases, the classical method is highly deteriorated, with significant bias and root mean squared error, while the proposed method demonstrates much better performance. Both methods are employed to fit the “working” 3-segment regression model and perform a plateau test on apparently contaminated oxygen uptake data. The results reveal that, due to the presence of outliers, the classical method produces inflated estimates for the error variance and larger standard errors for all parameters, in comparison to the proposed method. Moreover, the plateau test conducted using the classical (robust) method leads to the rejection (confirmation) of a plateau of oxygen uptake for the same data. Overall, these findings highlight the superiority of the proposed method in handling outliers.

RESUMO: O Estado do Espírito Santo sofreu vários surtos de dengue nasúltimas décadas, transformando essa doença em um grave problema de saúde pública. De acordo com o Ministério da Saúde, em 2013, o Estado ocupou o quinto lugar entre os onze Estados com maior incidência de dengue, já no ano de 2016, chegou a ocupar o terceiro lugar no ranking dos Estados em incidência da doença. O presente estudo propõe uma metodologia alternativa para a modelagem da incidência de dengue na Região da Grande Vitória (RGV) -Brasil, através do modelo ARMA espaço-temporal. O modelo mostrou-se bastante adequado para os dados aqui analisados. Foi identificada associação espacial e temporal, sendo que as taxas de incidência dos municípios são influenciadas diretamente pelas taxas observadas no período de até dois meses antes, tanto no município em questão quanto nos municípios vizinhos. PALAVRAS-CHAVE: Incidência de dengue; modelos espaço-temporais; modelo STARMA.