On the efficacy of techniques for evaluating multivariate volatility forecasts

The performance of techniques for evaluating multivariate volatility forecasts are not yet as well understood as their univariate counterparts. This paper aims to evaluate the efficacy of a range of traditional statistical-based methods for multivariate forecast evaluation together with methods based on underlying considerations of economic theory. It is found that a statistical-based method based on likelihood theory and an economic loss function based on portfolio variance are the most effective means of identifying optimal forecasts of conditional covariance matrices.

A multivariate approach to the identification of surrogate parameters for heavy metals in stormwater

Stormwater is a potential and readily available alternative source for potable water in urban areas. However, its direct use is severely constrained by the presence of toxic pollutants, such as heavy metals (HMs). The presence of HMs in stormwater is of concern because of their chronic toxicity and persistent nature. In addition to human health impacts, metals can contribute to adverse ecosystem health impact on receiving waters. Therefore, the ability to predict the levels of HMs in stormwater is crucial for monitoring stormwater quality and for the design of effective treatment systems. Unfortunately, the current laboratory methods for determining HM concentrations are resource intensive and time consuming. In this paper, applications of multivariate data analysis techniques are presented to identify potential surrogate parameters which can be used to determine HM concentrations in stormwater. Accordingly, partial least squares was applied to identify a suite of physicochemical parameters which can serve as indicators of HMs. Datasets having varied characteristics, such as land use and particle size distribution of solids, were analyzed to validate the efficacy of the influencing parameters. Iron, manganese, total organic carbon, and inorganic carbon were identified as the predominant parameters that correlate with the HM concentrations. The practical extension of the study outcomes to urban stormwater management is also discussed.

Linking three-dimensional geological modelling and multivariate statistical analysis to define groundwater chemistry baseline and identify inter-aquifer connectivity within the Clarence-Moreton Basin, Southeast Queensland, Australia

The Clarence-Moreton Basin (CMB) covers approximately 26000 km2 and is the only sub-basin of the Great Artesian Basin (GAB) in which there is flow to both the south-west and the east, although flow to the south-west is predominant. In many parts of the basin, including catchments of the Bremer, Logan and upper Condamine Rivers in southeast Queensland, the Walloon Coal Measures are under exploration for Coal Seam Gas (CSG). In order to assess spatial variations in groundwater flow and hydrochemistry at a basin-wide scale, a 3D hydrogeological model of the Queensland section of the CMB has been developed using GoCAD modelling software. Prior to any large-scale CSG extraction, it is essential to understand the existing hydrochemical character of the different aquifers and to establish any potential linkage. To effectively use the large amount of water chemistry data existing for assessment of hydrochemical evolution within the different lithostratigraphic units, multivariate statistical techniques were employed.

Regression and hypothesis tests for multivariate GNSS state time series

A satellite based observation system can continuously or repeatedly generate a user state vector time series that may contain useful information. One typical example is the collection of International GNSS Services (IGS) station daily and weekly combined solutions. Another example is the epoch-by-epoch kinematic position time series of a receiver derived by a GPS real time kinematic (RTK) technique. Although some multivariate analysis techniques have been adopted to assess the noise characteristics of multivariate state time series, statistic testings are limited to univariate time series. After review of frequently used hypotheses test statistics in univariate analysis of GNSS state time series, the paper presents a number of T-squared multivariate analysis statistics for use in the analysis of multivariate GNSS state time series. These T-squared test statistics have taken the correlation between coordinate components into account, which is neglected in univariate analysis. Numerical analysis was conducted with the multi-year time series of an IGS station to schematically demonstrate the results from the multivariate hypothesis testing in comparison with the univariate hypothesis testing results. The results have demonstrated that, in general, the testing for multivariate mean shifts and outliers tends to reject less data samples than the testing for univariate mean shifts and outliers under the same confidence level. It is noted that neither univariate nor multivariate data analysis methods are intended to replace physical analysis. Instead, these should be treated as complementary statistical methods for a prior or posteriori investigations. Physical analysis is necessary subsequently to refine and interpret the results.

A multivariate approach to bidding strategies

A multivariate approach to bidding strategy is presented in comparison with previous standard approaches. An optimal formulation is derived and a method of parameter estimation proposed. A case study illustrates the derivation of optimal and other strategic mark up values against a single bidder. Concluding remarks concern extensions to multiple competitors differing levels of information, and sensitivity analysis.

A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions

A quasi-maximum likelihood procedure for estimating the parameters of multi-dimensional diffusions is developed in which the transitional density is a multivariate Gaussian density with first and second moments approximating the true moments of the unknown density. For affine drift and diffusion functions, the moments are exactly those of the true transitional density and for nonlinear drift and diffusion functions the approximation is extremely good and is as effective as alternative methods based on likelihood approximations. The estimation procedure generalises to models with latent factors. A conditioning procedure is developed that allows parameter estimation in the absence of proxies.

Multivariate statistical analysis of hydrochemical data to assess alluvial aquifer–stream connectivity during drought and flood : Cressbrook Creek, southeast Queensland, Australia

A catchment-scale multivariate statistical analysis of hydrochemistry enabled assessment of interactions between alluvial groundwater and Cressbrook Creek, an intermittent drainage system in southeast Queensland, Australia. Hierarchical cluster analyses and principal component analysis were applied to time-series data to evaluate the hydrochemical evolution of groundwater during periods of extreme drought and severe flooding. A simple three-dimensional geological model was developed to conceptualise the catchment morphology and the stratigraphic framework of the alluvium. The alluvium forms a two-layer system with a basal coarse-grained layer overlain by a clay-rich low-permeability unit. In the upper and middle catchment, alluvial groundwater is chemically similar to streamwater, particularly near the creek (reflected by high HCO3/Cl and K/Na ratios and low salinities), indicating a high degree of connectivity. In the lower catchment, groundwater is more saline with lower HCO3/Cl and K/Na ratios, notably during dry periods. Groundwater salinity substantially decreased following severe flooding in 2011, notably in the lower catchment, confirming that flooding is an important mechanism for both recharge and maintaining groundwater quality. The integrated approach used in this study enabled effective interpretation of hydrological processes and can be applied to a variety of hydrological settings to synthesise and evaluate large hydrochemical datasets.

A public perspective on the adoption of microgeneration technologies in New Zealand: A multivariate probit approach

The growing demand for electricity in New Zealand has led to the construction of new hydro-dams or power stations that have had environmental, social and cultural effects. These effects may drive increases in electricity prices, as such prices reflect the cost of running existing power stations as well as building new ones. This study uses Canterbury and Central Otago as case studies because both regions face similar issues in building new hydro-dams and ever-increasing electricity prices that will eventually prompt households to buy power at higher prices. One way for households to respond to these price changes is to generate their own electricity through microgeneration technologies (MGT). The objective of this study is to investigate public perception and preferences regarding MGT and to analyze the factors that influence people's decision to adopt such new technologies in New Zealand. The study uses a multivariate probit approach to examine households' willingness to adopt any one MGT system or a combination of the MGT systems. Our findings provide valuable information for policy makers and marketers who wish to promote effective microgeneration technologies.

Hydrochemical evolution and groundwater flow processes in the Galilee and Eromanga basins, Great Artesian Basin, Australia: A multivariate statistical approach

The Galilee and Eromanga basins are sub-basins of the Great Artesian Basin (GAB). In this study, a multivariate statistical approach (hierarchical cluster analysis, principal component analysis and factor analysis) is carried out to identify hydrochemical patterns and assess the processes that control hydrochemical evolution within key aquifers of the GAB in these basins. The results of the hydrochemical assessment are integrated into a 3D geological model (previously developed) to support the analysis of spatial patterns of hydrochemistry, and to identify the hydrochemical and hydrological processes that control hydrochemical variability. In this area of the GAB, the hydrochemical evolution of groundwater is dominated by evapotranspiration near the recharge area resulting in a dominance of the Na–Cl water types. This is shown conceptually using two selected cross-sections which represent discrete groundwater flow paths from the recharge areas to the deeper parts of the basins. With increasing distance from the recharge area, a shift towards a dominance of carbonate (e.g. Na–HCO3 water type) has been observed. The assessment of hydrochemical changes along groundwater flow paths highlights how aquifers are separated in some areas, and how mixing between groundwater from different aquifers occurs elsewhere controlled by geological structures, including between GAB aquifers and coal bearing strata of the Galilee Basin. The results of this study suggest that distinct hydrochemical differences can be observed within the previously defined Early Cretaceous–Jurassic aquifer sequence of the GAB. A revision of the two previously recognised hydrochemical sequences is being proposed, resulting in three hydrochemical sequences based on systematic differences in hydrochemistry, salinity and dominant hydrochemical processes. The integrated approach presented in this study which combines different complementary multivariate statistical techniques with a detailed assessment of the geological framework of these sedimentary basins, can be adopted in other complex multi-aquifer systems to assess hydrochemical evolution and its geological controls.

An efficient DSE using conditional multivariate complex Gaussian distribution

This paper presents an efficient noniterative method for distribution state estimation using conditional multivariate complex Gaussian distribution (CMCGD). In the proposed method, the mean and standard deviation (SD) of the state variables is obtained in one step considering load uncertainties, measurement errors, and load correlations. In this method, first the bus voltages, branch currents, and injection currents are represented by MCGD using direct load flow and a linear transformation. Then, the mean and SD of bus voltages, or other states, are calculated using CMCGD and estimation of variance method. The mean and SD of pseudo measurements, as well as spatial correlations between pseudo measurements, are modeled based on the historical data for different levels of load duration curve. The proposed method can handle load uncertainties without using time-consuming approaches such as Monte Carlo. Simulation results of two case studies, six-bus, and a realistic 747-bus distribution network show the effectiveness of the proposed method in terms of speed, accuracy, and quality against the conventional approach.

The multivariate A/C/E model and the genetics of fiber architecture

We present a new algorithm to compute the voxel-wise genetic contribution to brain fiber microstructure using diffusion tensor imaging (DTI) in a dataset of 25 monozygotic (MZ) twins and 25 dizygotic (DZ) twin pairs (100 subjects total). First, the structural and DT scans were linearly co-registered. Structural MR scans were nonlinearly mapped via a 3D fluid transformation to a geometrically centered mean template, and the deformation fields were applied to the DTI volumes. After tensor re-orientation to realign them to the anatomy, we computed several scalar and multivariate DT-derived measures including the geodesic anisotropy (GA), the tensor eigenvalues and the full diffusion tensors. A covariance-weighted distance was measured between twins in the Log-Euclidean framework [2], and used as input to a maximum-likelihood based algorithm to compute the contributions from genetics (A), common environmental factors (C) and unique environmental ones (E) to fiber architecture. Quanititative genetic studies can take advantage of the full information in the diffusion tensor, using covariance weighted distances and statistics on the tensor manifold.

Multivariate variance-components analysis in DTI

Twin studies are a major research direction in imaging genetics, a new field, which combines algorithms from quantitative genetics and neuroimaging to assess genetic effects on the brain. In twin imaging studies, it is common to estimate the intraclass correlation (ICC), which measures the resemblance between twin pairs for a given phenotype. In this paper, we extend the commonly used Pearson correlation to a more appropriate definition, which uses restricted maximum likelihood methods (REML). We computed proportion of phenotypic variance due to additive (A) genetic factors, common (C) and unique (E) environmental factors using a new definition of the variance components in the diffusion tensor-valued signals. We applied our analysis to a dataset of Diffusion Tensor Images (DTI) from 25 identical and 25 fraternal twin pairs. Differences between the REML and Pearson estimators were plotted for different sample sizes, showing that the REML approach avoids severe biases when samples are smaller. Measures of genetic effects were computed for scalar and multivariate diffusion tensor derived measures including the geodesic anisotropy (tGA) and the full diffusion tensors (DT), revealing voxel-wise genetic contributions to brain fiber microstructure.

Identifying candidate gene effects by restricting search space in a multivariate genetic analysis of white matter microstructure

Several genetic variants are thought to influence white matter (WM) integrity, measured with diffusion tensor imaging (DTI). Voxel based methods can test genetic associations, but heavy multiple comparisons corrections are required to adjust for searching the whole brain and for all genetic variants analyzed. Thus, genetic associations are hard to detect even in large studies. Using a recently developed multi-SNP analysis, we examined the joint predictive power of a group of 18 cholesterol-related single nucleotide polymorphisms (SNPs) on WM integrity, measured by fractional anisotropy. To boost power, we limited the analysis to brain voxels that showed significant associations with total serum cholesterol levels. From this space, we identified two genes with effects that replicated in individual voxel-wise analyses of the whole brain. Multivariate analyses of genetic variants on a reduced anatomical search space may help to identify SNPs with strongest effects on the brain from a broad panel of genes.