We propose a state-space approach for GARCH models with time-varying parameters able to deal with non-stationarity that is usually observed in a wide variety of time series. The parameters of the non-stationary model are allowed to vary smoothly over time through non-negative deterministic functions. We implement the estimation of the time-varying parameters in the time domain through Kalman filter recursive equations, finding a state-space representation of a class of time-varying GARCH models. We provide prediction intervals for time-varying GARCH models and, additionally, we propose a simple methodology for handling missing values. Finally, the proposed methodology is applied to the Chilean Stock Market (IPSA) and to the American Standard&Poor's 500 index (S&P500).

The family of logistic type distributions has been widely studied and applied in the literature. However, certain estimation problems exist in some members of this family. Particularly, the three-parameter type I generalized logistic distribution presents these problems, where the parameter space must be restricted for the existence of their maximum likelihood estimators. In this paper, motivated by the complexities that arise in the inference under the likelihood approach utilizing this distribution, we propose a Bayesian approach to solve these problems. A simulation study is carried out to assess the performance of some posterior distributional characteristics, such as the mean, using Monte Carlo Markov chain methods. To illustrate the potentiality of the Bayesian estimation in the three-parameter type I generalized logistic distribution, we apply the proposed method to real-world data related to the copper metallurgical engineering area.

Extensive research has been conducted on models that utilize the Kumaraswamy distribution to describe continuous variables with bounded support. In this study, we examine the trapezoidal Kumaraswamy model. Our objective is to propose a parameter estimation method for this model using the stochastic expectation maximization algorithm, which effectively tackles the challenges commonly encountered in the traditional expectation maximization algorithm. We then apply our results to the modeling of daily COVID-19 cases in Chile.

Multiple chronic conditions are an important factor influencing mortality in older adults. At the same time, cardiovascular events in older adult patients are one of the leading causes of mortality worldwide. This study aimed to design a machine learning model capable of predicting mortality risk in older adult patients with cardiovascular pathologies and multiple chronic diseases using the Cardiovascular Health Study database. The methodology for algorithm design included (i) database analysis, (ii) variable selection, (iii) feature matrix creation and data preprocessing, (iv) model training, and (v) performance analysis. The analysis and variable selection were performed through previous knowledge, correlation, and histograms to visualize the data distribution. The machine learning models selected were random forest, support vector machine, and logistic regression. The models were trained using two sets of variables. First, eight years of the data were summarized as the mode of all years per patient for each variable (123 variables). The second set of variables was obtained from the mode every three years (369 variables). The results show that the random forest trained with the second set of variables has the best performance (89% accuracy), which is better than other reported results in the literature.

Although several studies have documented the detrimental impacts of global COVID-19 containment measures on individuals with Alzheimer's disease and dementia, a comprehensive analysis of mortality rates for these conditions within the Chilean population is notably lacking. This study aimed to analyze the impact of COVID-19 on mortality rates among individuals with dementia and Alzheimer's disease in Chile. A retrospective longitudinal cross-sectional study was conducted, considering mortality data for specific mental health conditions during the pre-pandemic and pandemic contexts of COVID-19 in Chile. Quantile regression techniques were employed to analyze the existence of differences between the two periods, while non-observable heterogeneity models for panel data methods were used to evaluate the effect of COVID-19 mortality on crude mortality rates. Statistically significant differences were observed in the number of deaths from dementia and Alzheimer’s disease between the pre-pandemic and COVID-19 pandemic periods. Specifically, crude mortality rates decreased by 10% (−0.10 [95% CI: −0.16, −0.05]) during the pandemic period. Furthermore, the number of deaths from COVID-19 during the pandemic period has a very weak incidence of deaths from mental health conditions such as dementia and Alzheimer’s. Specifically, a unit percentage increase in confirmed cases from COVID-19 would result in a 7% (−0.07 [95% CI: −0.13, −0.001]) decrease in the number of deaths from dementia and Alzheimer’s. These findings are supported by the application of panel regression with one-way random effects models. The study findings indicate a reduction in mortality rates attributed to dementia and Alzheimer’s disease during the COVID-19 pandemic in Chile. This decline could be attributed to the potential underreporting of mental illness as the cause of death during the pandemic period. Several studies have highlighted that approximately 30% of death certificates fail to document the presence of a dementia syndrome. Moreover, the cause of death recorded for individuals with mental health conditions may be influenced by the physician’s familiarity with the patient or reflect the prevailing approach to managing end-stage dementia patients. This work received no funding.

Purpose: This study aims to develop a structured methodology for selecting and ranking frequency-domain vibration features to assess the severity of failure in spur gearboxes, taking into account the effects of sensor position and inclination. Methods: Vibration signals were acquired from six accelerometers installed with varying spatial positions and inclinations on the gearbox housing. The signals were transformed into the frequency domain via Fast Fourier Transform (FFT), from which 25 condition indicators (CIs) were extracted. A two-step feature ranking strategy was implemented using effect size (Cohen’s d) and classification performance from Random Forest (RF) and K-Nearest Neighbors (KNN). Subsequently, Mahalanobis distance was employed to assess multivariate separation, and factorial ANOVA was used to evaluate the impact of sensor placement and inclination. Results: The Third Moment, Fourth Moment, and Central Frequency emerged as the most discriminative features across different fault types and severity levels. Mahalanobis distance increased with fault progression, confirming the effectiveness of the selected features for degradation tracking. Although sensor position and inclination introduced some variability, their influence on classification accuracy was limited. Conclusions: The proposed methodology enables interpretable and robust feature selection forcondition monitoring of gearboxes. It enhances diagnostic reliability while demonstrating resilience to sensor placement variability, making it suitable for practical industrial implementations.