We introduce a new approach for comparing the predictive accuracy of two nested models that bypasses the difficulties caused by the degeneracy of the asymptotic variance of forecast error loss differentials used in the construction of commonly used predictive comparison statistics. Our approach continues to rely on the out of sample mean squared error loss differentials between the two competing models, leads to nuisance parameter-free Gaussian asymptotics, and is shown to remain valid under flexible assumptions that can accommodate heteroskedasticity and the presence of mixed predictors (e.g., stationary and local to unit root). A local power analysis also establishes their ability to detect departures from the null in both stationary and persistent settings. Simulations calibrated to common economic and financial applications indicate that our methods have strong power with good size control across commonly encountered sample sizes.

We extend the notion of universal graphs to a geometric setting. A geometric graph is universal for a class $\mathcal H$ of planar graphs if it contains an embedding, that is, a crossing-free drawing, of every graph in $\mathcal H$. Our main result is that there exists a geometric graph with $n$ vertices and $O\!\left(n \log n\right)$ edges that is universal for $n$-vertex forests; this generalises a well-known result by Chung and Graham, which states that there exists an (abstract) graph with $n$ vertices and $O\!\left(n \log n\right)$ edges that contains every $n$-vertex forest as a subgraph. The upper bound of $O\!\left(n \log n\right)$ edges cannot be improved, even if more than $n$ vertices are allowed. We also prove that every $n$-vertex convex geometric graph that is universal for $n$-vertex outerplanar graphs has a near-quadratic number of edges, namely $\Omega _h(n^{2-1/h})$, for every positive integer $h$; this almost matches the trivial $O(n^2)$ upper bound given by the $n$-vertex complete convex geometric graph. Finally, we prove that there exists an $n$-vertex convex geometric graph with $n$ vertices and $O\!\left(n \log n\right)$ edges that is universal for $n$-vertex caterpillars.

Since the discovery of Legionnaires’ disease (LD), limited progress has been made in understanding the epidemiology of sporadic cases of LD. Outbreaks have confirmed that air conditioning and potable water systems can be sources of community-acquired LD. However, studying the association between water quality and LD incidence has been challenging due to the heterogeneity of water systems across large geographic areas. Furthermore, although seasonal trends in incidence have been linked to increased rainfall and temperatures, the large geographic units have posed similar difficulties. To address this issue, a retrospective ecological study was conducted in Washington, DC, from 2001 to 2019. The study identified aseasonal pattern of LD incidence, with the majority of cases occurring between June and December, peaking in August, October, and November. Increased temperature was found to be associated with LD incidence. In surface water, higher concentrations of manganese, iron, and strontium were positively associated with LD, while aluminum and orthophosphate showed a negative association. Intreatment plant water, higher concentrations of total organic carbon, aluminum, barium, and chlorine were positively associated with LD, while strontium, zinc, and orthophosphate showed a negative association. The results for orthophosphates and turbidity were inconclusive, indicating the need for further research.

We establish new results on the strictly stationary solution to an iterated function system. When the driving sequence is stationary and ergodic, though not independent, the strictly stationary solution may admit no moment but we show an exponential control of the trajectories. We exploit these results to prove, under mild conditions, the consistency of the quasi-maximum likelihood estimator of GARCH(p,q) models with non-independent innovations.

In GARCH-mixed-data sampling models, the volatility is decomposed into the product of two factors which are often interpreted as “short-run” (high-frequency) and “long-run” (low-frequency) components. While two-component volatility models are widely used in applied works, some of their theoretical properties remain unexplored. We show that the strictly stationary solutions of such models do not admit any small-order finite moment, contrary to classical GARCH. It is shown that the strong consistency and the asymptotic normality of the quasi-maximum likelihood estimator hold despite the absence of moments. Tests for the presence of a long-run volatility relying on the asymptotic theory and a bootstrap procedure are proposed. Our results are illustrated via Monte Carlo experiments and real financial data.

Parkinson’s disease (PD) is an irreversible neurodegenerative disorder clinically manifesting in uncontrolled motor symptoms. There are two primary hallmark features of Parkinson’s disease—an irreversible loss of dopaminergic neurons of the substantia nigra pars compacta and formation of intracellular insoluble aggregates called Lewy bodies mostly composed of alpha-synuclein. Using a clinical improvements-first approach, we identified several clinical trials involving consumption of a specific diet or nutritional supplementation that improved motor and nonmotor functions. Here, we aimed to investigate if and how pyrroloquinoline quinone (PQQ) compound disrupts preformed alpha-synuclein deposits using SH-SY5Y cells, widely used Parkinson’s disease cellular model. SH-SY5Y neuroblastoma cells, incubated in presence of potassium chloride (KCl) to induce alpha-synuclein protein aggregation, were treated with PQQ for up to 48 hr. Resulting aggregates were examined and quantified using confocal microscopy. Overall, nutritional compound PQQ reduced the average number and overall size of intracellular cytoplasmic alpha-synuclein aggregates in a PD cellular model.