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.

Calibration functions for estimating soil moisture from GPR dielectric constant measurements

Ground-penetrating radar (GPR) is widely used for assessment of soil moisture variability in field soils. Because GPR does not measure soil water content directly, it is common practice to use calibration functions that describe its relationship with the soil dielectric properties and textural parameters. However, the large variety of models complicates the selection of the appropriate function. In this article an overview is presented of the different functions available, including volumetric models, empirical functions, effective medium theories, and frequency-specific functions. Using detailed information presented in summary tables, the choice for which calibration function to use can be guided by the soil variables available to the user, the frequency of the GPR equipment, and the desired level of detail of the output. This article can thus serve as a guide for GPR practitioners to obtain soil moisture values and to estimate soil dielectric properties.

Model choice problems using approximate Bayesian computation with applications to pathogen transmission data sets

Analytically or computationally intractable likelihood functions can arise in complex statistical inferential problems making them inaccessible to standard Bayesian inferential methods. Approximate Bayesian computation (ABC) methods address such inferential problems by replacing direct likelihood evaluations with repeated sampling from the model. ABC methods have been predominantly applied to parameter estimation problems and less to model choice problems due to the added difficulty of handling multiple model spaces. The ABC algorithm proposed here addresses model choice problems by extending Fearnhead and Prangle (2012, Journal of the Royal Statistical Society, Series B 74, 1–28) where the posterior mean of the model parameters estimated through regression formed the summary statistics used in the discrepancy measure. An additional stepwise multinomial logistic regression is performed on the model indicator variable in the regression step and the estimated model probabilities are incorporated into the set of summary statistics for model choice purposes. A reversible jump Markov chain Monte Carlo step is also included in the algorithm to increase model diversity for thorough exploration of the model space. This algorithm was applied to a validating example to demonstrate the robustness of the algorithm across a wide range of true model probabilities. Its subsequent use in three pathogen transmission examples of varying complexity illustrates the utility of the algorithm in inferring preference of particular transmission models for the pathogens.

The Expanded Human Kallikrein (KLK) gene family : genomic organisation, tissue specific expression and potential functions

The tissue kallikreins are serine proteases encoded by highly conserved multigene families. The rodent kallikrein (KLK) families are particularly large, consisting of 13 26 genes clustered in one chromosomal locus. It has been recently recognised that the human KLK gene family is of a similar size (15 genes) with the identification of another 12 related genes (KLK4-KLK15) within and adjacent to the original human KLK locus (KLK1-3) on chromosome 19q13.4. The structural organisation and size of these new genes is similar to that of other KLK genes except for additional exons encoding 5 or 3 untranslated regions. Moreover, many of these genes have multiple mRNA transcripts, a trait not observed with rodent genes. Unlike all other kallikreins, the KLK4-KLK15 encoded proteases are less related (25–44%) and do not contain a conventional kallikrein loop. Clusters of genes exhibit high prostatic (KLK2-4, KLK15) or pancreatic (KLK6-13) expression, suggesting evolutionary conservation of elements conferring tissue specificity. These genes are also expressed, to varying degrees, in a wider range of tissues suggesting a functional involvement of these newer human kallikrein proteases in a diverse range of physiological processes.

Sexual selection in a tropical fruit fly : role of a plant derived chemical in mate choice

The specific mechanisms by which selective pressures affect individuals are often difficult to resolve. In tephritid fruit flies, males respond strongly and positively to certain plant derived chemicals. Sexual selection by female choice has been hypothesized as the mechanism driving this behaviour in certain species, as females preferentially mate with males that have fed on these chemicals. This hypothesis is, to date, based on studies of only very few species and its generality is largely untested. We tested the hypothesis on different spatial scales (small cage and seminatural field-cage) using the monophagous fruit fly, Bactrocera cacuminata. This species is known to respond to methyl eugenol (ME), a chemical found in many plant species and one upon which previous studies have focused. Contrary to expectation, no obvious female choice was apparent in selecting ME-fed males over unfed males as measured by the number of matings achieved over time, copulation duration, or time of copulation initiation. However, the number of matings achieved by ME-fed males was significantly greater than unfed males 16 and 32 days after exposure to ME in small cages (but not in a field-cage). This delayed advantage suggests that ME may not influence the pheromone system of B. cacuminata but may have other consequences, acting on some other fitness consequence (e.g., enhancement of physiology or survival) of male exposure to these chemicals. We discuss the ecological and evolutionary implications of our findings to explore alternate hypotheses to explain the patterns of response of dacine fruit flies to specific plant-derived chemicals.