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This paper extends the conditional autoregressive range (CARR) model to the multivariate CARR (MCARR) model and further to the two-stage MCARR-return model to model and forecast volatilities, correlations and returns of multiple financial assets. The first stage model fits the scaled realised Parkinson volatility measures using individual series and their pairwise sums of indices to the MCARR model to obtain the fitted volatilities. Then covariances are calculated to construct the fitted variance–covariance matrix of returns which are imputed into the stage-two return model to capture the heteroskedasticity of assets' returns. We investigate different choices of mean functions to describe the volatility dynamics. Empirical applications are based on the Standard and Poor 500, Dow Jones Industrial Average and Dow Jones United States Financial Service Indices. Results show that the stage-one MCARR models using asymmetric mean functions give better in-sample model fits than those based on symmetric mean functions. They also provide better out-of-sample volatility forecasts than those using CARR models based on two robust loss functions. We also find that the stage-two return models with constant means and multivariate Student-t errors give better in-sample fits than the Baba–Engle–Kraft–Kroner generalised autoregressive conditional heteroskedasticity models. The estimates and forecasts of value-at-risk (VaR) and conditional VaR based on the best MCARR-return models for each asset are provided and tested using backtests to confirm the accuracy of the VaR forecasts. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of finding the optimal routing policies with only trajectory information in a stochastic time-dependent network where all link travel times are temporally and spatially correlated. Two equivalent definitions are given for trajectory-adaptive routing policy. The first definition follows the mapping definition in a series of previous studies, where the trajectory information is included in the state variable. With that definition, any subpolicy of an optimal routing policy must also be optimal, and the algorithm developed in previous studies could serve as an exact solution, but the nature of the definition that trajectory information is included in the state variable determines that the number of states is prohibitively huge. Therefore, a second definition is given as a recursive definition, where the trajectory information is not included in the state variable. It is shown that, with the second definition, a subpolicy of an optimal/nondominated routing policy is not necessarily optimal/nondominated, but any subpolicy of a pure routing policy must also be pure which is a new property defined based on nondominance. An exact algorithm is designed to find optimal trajectory-adaptive routing policies based on the aforementioned property of pure routing policy. A comparison is made between the optimal trajectory-adaptive routing policies and the optimal paths in the same test networks to investigate the benefit of being adaptive. The results show that the benefit of being adaptive to trajectory information is more significant with a higher risk aversion, a higher correlation, and/or a larger network. [ABSTRACT FROM AUTHOR]

In a recent paper, Leroux compared three satellite soil moisture data sets (SMOS, AMSR-E, and ASCAT) and ECMWF forecast soil moisture data to in situ measurements over four watersheds located in the United States. Their conclusions stated that SMOS soil moisture retrievals represent “an improvement [in RMSE] by a factor of 2-3 compared with the other products” and that the ASCAT soil moisture data are “very noisy and unstable.” In this clarification, the analysis of Leroux is repeated using a newer version of the ASCAT data and additional metrics are provided. It is shown that the ASCAT retrievals are skillful, although they show some unexpected behavior during summer for two of the watersheds. It is also noted that the improvement of SMOS by a factor of 2-3 mentioned by Leroux is driven by differences in bias and only applies relative to AMSR-E and the ECWMF data in the now obsolete version investigated by Leroux et al. [ABSTRACT FROM PUBLISHER]

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly related to creativity in mathematics, too. This paper reports on a study that investigated USA and Chinese high school students' mathematical content knowledge, their abilities in mathematical problem posing, and the relationships between students' mathematical content knowledge and their problem-posing abilities in mathematics. [ABSTRACT FROM AUTHOR]

Bivariate correlation analysis has been widely used to explore relationships between stream and watershed attributes that have all been measured on the same set of watersheds or sampling locations. Researchers routinely test H[sub0]: ρ = 0 for each correlation in a large table and then go on to discuss only those that are declared "significant." Such test results are inaccurate because no allowance is made for multiple testing, and also because the tests are not mutually independent. This paper reviews the Bonferroni approach to controlling the overall error rate in multiple testing and shows how the approach becomes impractical for large correlation tables. The Hotelling/Williams test is introduced for comparing two dependent correlations that share a variable, and numerical constraints for two such correlations are illustrated. References are also given for testing other hypothesized patterns among dependent correlations, and links to dependent correlation software are provided. The methods are illustrated for watershed and stream variables sampled in 23 small agricultural watersheds of the Willamette Valley, Oregon. [ABSTRACT FROM AUTHOR]