Quasi-maximum likelihood estimation and bootstrap inference in fractional time series models with heteroskedasticity of unknown form

We consider the problem of conducting estimation and inference on the parameters of univariate heteroskedastic fractionally integrated time series models. We first extend existing results in the literature, developed for conditional sum-of-squares estimators in the context of parametric fractional time series models driven by conditionally homoskedastic shocks, to allow for conditional and unconditional heteroskedasticity both of a quite general and unknown form. Global consistency and asymptotic normality are shown to still obtain; however, the covariance matrix of the limiting distribution of the estimator now depends on nuisance parameters derived both from the weak dependence and heteroskedasticity present in the shocks. We then investigate classical methods of inference based on the Wald, likelihood ratio and Lagrange multiplier tests for linear hypotheses on either or both of the long and short memory parameters of the model. The limiting null distributions of these test statistics are shown to be non-pivotal under heteroskedasticity, while that of a robust Wald statistic (based around a sandwich estimator of the variance) is pivotal. We show that wild bootstrap implementations of the tests deliver asymptotically pivotal inference under the null. We demonstrate the consistency and asymptotic normality of the bootstrap estimators, and further establish the global consistency of the asymptotic and bootstrap tests under fixed alternatives. Monte Carlo simulations highlight significant improvements in finite sample behavior using the bootstrap in both heteroskedastic and homoskedastic environments. Our theoretical developments and Monte Carlo simulations include two bootstrap algorithms which are based on model estimates obtained either under the null hypothesis or unrestrictedly. Our simulation results suggest that the former is preferable to the latter, displaying superior size control yet largely comparable power

Role of age and comorbidities in mortality of patients with infective endocarditis

Purpose: The aim of this study was to analyse the characteristics of patients with IE in three groups of age and to assess the ability of age and the Charlson Comorbidity Index (CCI) to predict mortality. Methods: Prospective cohort study of all patients with IE included in the GAMES Spanish database between 2008 and 2015. Patients were stratified into three age groups:<65 years, 65 to 80 years, and = 80 years.The area under the receiver-operating characteristic (AUROC) curve was calculated to quantify the diagnostic accuracy of the CCI to predict mortality risk. Results: A total of 3120 patients with IE (1327 < 65 years;1291 65-80 years;502 = 80 years) were enrolled.Fever and heart failure were the most common presentations of IE, with no differences among age groups.Patients =80 years who underwent surgery were significantly lower compared with other age groups (14.3%, 65 years; 20.5%, 65-79 years; 31.3%, =80 years). In-hospital mortality was lower in the <65-year group (20.3%, <65 years;30.1%, 65-79 years;34.7%, =80 years;p < 0.001) as well as 1-year mortality (3.2%, <65 years; 5.5%, 65-80 years;7.6%, =80 years; p = 0.003).Independent predictors of mortality were age = 80 years (hazard ratio [HR]:2.78;95% confidence interval [CI]:2.32–3.34), CCI = 3 (HR:1.62; 95% CI:1.39–1.88), and non-performed surgery (HR:1.64;95% CI:11.16–1.58).When the three age groups were compared, the AUROC curve for CCI was significantly larger for patients aged <65 years(p < 0.001) for both in-hospital and 1-year mortality. Conclusion: There were no differences in the clinical presentation of IE between the groups. Age = 80 years, high comorbidity (measured by CCI), and non-performance of surgery were independent predictors of mortality in patients with IE.CCI could help to identify those patients with IE and surgical indication who present a lower risk of in-hospital and 1-year mortality after surgery, especially in the <65-year group