In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it is nonparametric, the procedure avoids the difficulties associated with parametric model selection, model fitting and parameter estimation. We provide the theoretical foundation for the test and demonstrate its applicability via a simulation study and an analysis of financial data. Extensions to multiple changes and the case of infinite fourth moments are also discussed.

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Gut and oral microbiota perturbations have been observed in obese adults and adolescents; less is known about their influence on weight gain in young children. Here we analyzed the gut and oral microbiota of 226 two-year-olds with 16S rRNA gene sequencing. Weight and length were measured at seven time points and used to identify children with rapid infant weight gain (a strong risk factor for childhood obesity), and to derive growth curves with innovative Functional Data Analysis (FDA) techniques. We showed that growth curves were associated negatively with diversity, and positively with the Firmicutes-to-Bacteroidetes ratio, of the oral microbiota. We also demonstrated an association between the gut microbiota and child growth, even after controlling for the effect of diet on the microbiota. Lastly, we identified several bacterial genera that were associated with child growth patterns. These results suggest that by the age of two, the oral microbiota of children with rapid infant weight gain may have already begun to establish patterns often seen in obese adults. They also suggest that the gut microbiota at age two, while strongly influenced by diet, does not harbor obesity signatures many researchers identified in later life stages.

The paper develops inferential methodology for detecting a change in the annual pattern of an environmental variable measured at fixed locations in a spatial region. Using a framework built on functional data analysis, we model observations as a collection of functionvalued time sequences available at many sites. Each sequence is modelled as an annual mean function, which may change, plus a sequence of error functions, which are spatially correlated.The tests statistics extend the cumulative sum paradigm to this more complex setting. Their asymptotic distributions are not parameter free because of the spatial dependence but can be effectively approximated by Monte Carlo simulations. The new methodology is applied to precipitation data. Its finite sample performance is assessed by a simulation study.

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