Evaluating multivariate volatility forecasts : how effective are statistical and economic loss functions?

Multivariate volatility forecasts are an important input in many financial applications, in particular portfolio optimisation problems. Given the number of models available and the range of loss functions to discriminate between them, it is obvious that selecting the optimal forecasting model is challenging. The aim of this thesis is to thoroughly investigate how effective many commonly used statistical (MSE and QLIKE) and economic (portfolio variance and portfolio utility) loss functions are at discriminating between competing multivariate volatility forecasts. An analytical investigation of the loss functions is performed to determine whether they identify the correct forecast as the best forecast. This is followed by an extensive simulation study examines the ability of the loss functions to consistently rank forecasts, and their statistical power within tests of predictive ability. For the tests of predictive ability, the model confidence set (MCS) approach of Hansen, Lunde and Nason (2003, 2011) is employed. As well, an empirical study investigates whether simulation findings hold in a realistic setting. In light of these earlier studies, a major empirical study seeks to identify the set of superior multivariate volatility forecasting models from 43 models that use either daily squared returns or realised volatility to generate forecasts. This study also assesses how the choice of volatility proxy affects the ability of the statistical loss functions to discriminate between forecasts. Analysis of the loss functions shows that QLIKE, MSE and portfolio variance can discriminate between multivariate volatility forecasts, while portfolio utility cannot. An examination of the effective loss functions shows that they all can identify the correct forecast at a point in time, however, their ability to discriminate between competing forecasts does vary. That is, QLIKE is identified as the most effective loss function, followed by portfolio variance which is then followed by MSE. The major empirical analysis reports that the optimal set of multivariate volatility forecasting models includes forecasts generated from daily squared returns and realised volatility. Furthermore, it finds that the volatility proxy affects the statistical loss functions’ ability to discriminate between forecasts in tests of predictive ability. These findings deepen our understanding of how to choose between competing multivariate volatility forecasts.

Non-invasive, quantitative analysis of drug mixtures in containers using spatially offset Raman spectroscopy (SORS) and multivariate statistical analysis

In this paper, spatially offset Raman spectroscopy (SORS) is demonstrated for non-invasively investigating the composition of drug mixtures inside an opaque plastic container. The mixtures consisted of three components including a target drug (acetaminophen or phenylephrine hydrochloride) and two diluents (glucose and caffeine). The target drug concentrations ranged from 5% to 100%. After conducting SORS analysis to ascertain the Raman spectra of the concealed mixtures, principal component analysis (PCA) was performed on the SORS spectra to reveal trends within the data. Partial least squares (PLS) regression was used to construct models that predicted the concentration of each target drug, in the presence of the other two diluents. The PLS models were able to predict the concentration of acetaminophen in the validation samples with a root-mean-square error of prediction (RMSEP) of 3.8% and the concentration of phenylephrine hydrochloride with an RMSEP of 4.6%. This work demonstrates the potential of SORS, used in conjunction with multivariate statistical techniques, to perform non-invasive, quantitative analysis on mixtures inside opaque containers. This has applications for pharmaceutical analysis, such as monitoring the degradation of pharmaceutical products on the shelf, in forensic investigations of counterfeit drugs, and for the analysis of illicit drug mixtures which may contain multiple components.

Three-dimensional geological modelling and multivariate statistical analysis of water chemistry data to analyse and visualise aquifer structure and groundwater composition in the Wairau Plain, Marlborough District, New Zealand

Concerns regarding groundwater contamination with nitrate and the long-term sustainability of groundwater resources have prompted the development of a multi-layered three dimensional (3D) geological model to characterise the aquifer geometry of the Wairau Plain, Marlborough District, New Zealand. The 3D geological model which consists of eight litho-stratigraphic units has been subsequently used to synthesise hydrogeological and hydrogeochemical data for different aquifers in an approach that aims to demonstrate how integration of water chemistry data within the physical framework of a 3D geological model can help to better understand and conceptualise groundwater systems in complex geological settings. Multivariate statistical techniques(e.g. Principal Component Analysis and Hierarchical Cluster Analysis) were applied to groundwater chemistry data to identify hydrochemical facies which are characteristic of distinct evolutionary pathways and a common hydrologic history of groundwaters. Principal Component Analysis on hydrochemical data demonstrated that natural water-rock interactions, redox potential and human agricultural impact are the key controls of groundwater quality in the Wairau Plain. Hierarchical Cluster Analysis revealed distinct hydrochemical water quality groups in the Wairau Plain groundwater system. Visualisation of the results of the multivariate statistical analyses and distribution of groundwater nitrate concentrations in the context of aquifer lithology highlighted the link between groundwater chemistry and the lithology of host aquifers. The methodology followed in this study can be applied in a variety of hydrogeological settings to synthesise geological, hydrogeological and hydrochemical data and present them in a format readily understood by a wide range of stakeholders. This enables a more efficient communication of the results of scientific studies to the wider community.

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.