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In this paper, we examine the S&P 500 index log-returns on short intraday time scales with three different ARMA-GARCH models. In order to forecast market risk, we describe the innovation process with tempered stable distributions which we compare to commonly used methods in financial modeling. Value-at-risk backtests are provided where we find that models based on the tempered stable innovation assumption significantly outperform traditional models in forecasting risk on short time-scales. In addition to value-at-risk, the idiosyncratic differences in average value-at-risk are compared between the models. [ABSTRACT FROM AUTHOR]

Importance: Few population-based studies in the US collected individual-level data from families during the COVID-19 pandemic., Objective: To examine differences in COVID-19 pandemic-related experiences in a large sociodemographically diverse sample of children and caregivers., Design, Setting, and Participants: The Environmental influences on Child Health Outcomes (ECHO) multi-cohort consortium is an ongoing study that brings together 64 individual cohorts with participants (24 757 children and 31 700 caregivers in this study) in all 50 US states and Puerto Rico. Participants who completed the ECHO COVID-19 survey between April 2020 and March 2022 were included in this cross-sectional analysis. Data were analyzed from July 2021 to September 2022., Main Outcomes and Measures: Exposures of interest were caregiver education level, child life stage (infant, preschool, middle childhood, and adolescent), and urban or rural (population <50 000) residence. Dependent variables included COVID-19 infection status and testing; disruptions to school, child care, and health care; financial hardships; and remote work. Outcomes were examined separately in logistic regression models mutually adjusted for exposures of interest and race, ethnicity, US Census division, sex, and survey administration date., Results: Analyses included 14 646 children (mean [SD] age, 7.1 [4.4] years; 7120 [49%] female) and 13 644 caregivers (mean [SD] age, 37.6 [7.2] years; 13 381 [98%] female). Caregivers were racially (3% Asian; 16% Black; 12% multiple race; 63% White) and ethnically (19% Hispanic) diverse and comparable with the US population. Less than high school education (vs master's degree or more) was associated with more challenges accessing COVID-19 tests (adjusted odds ratio [aOR], 1.88; 95% CI, 1.06-1.58), lower odds of working remotely (aOR, 0.04; 95% CI, 0.03-0.07), and more food access concerns (aOR, 4.14; 95% CI, 3.20-5.36). Compared with other age groups, young children (age 1 to 5 years) were least likely to receive support from schools during school closures, and their caregivers were most likely to have challenges arranging childcare and concerns about work impacts. Rural caregivers were less likely to rank health concerns (aOR, 0.77; 95% CI, 0.69-0.86) and social distancing (aOR, 0.82; 95% CI, 0.73-0.91) as top stressors compared with urban caregivers., Conclusions: Findings in this cohort study of US families highlighted pandemic-related burdens faced by families with lower socioeconomic status and young children. Populations more vulnerable to public health crises should be prioritized in recovery efforts and future planning.