Modeling Asymmetries in Financial Data with Multiplicative Error Models

This thesis addresses modeling of financial time series, especially stock market returns and daily price ranges. Modeling data of this kind can be approached with so-called multiplicative error models (MEM). These models nest several well known time series models such as GARCH, ACD and CARR models. They are able to capture many well established features of financial time series including volatility clustering and leptokurtosis. In contrast to these phenomena, different kinds of asymmetries have received relatively little attention in the existing literature. In this thesis asymmetries arise from various sources. They are observed in both conditional and unconditional distributions, for variables with non-negative values and for variables that have values on the real line. In the multivariate context asymmetries can be observed in the marginal distributions as well as in the relationships of the variables modeled. New methods for all these cases are proposed. Chapter 2 considers GARCH models and modeling of returns of two stock market indices. The chapter introduces the so-called generalized hyperbolic (GH) GARCH model to account for asymmetries in both conditional and unconditional distribution. In particular, two special cases of the GARCH-GH model which describe the data most accurately are proposed. They are found to improve the fit of the model when compared to symmetric GARCH models. The advantages of accounting for asymmetries are also observed through Value-at-Risk applications. Both theoretical and empirical contributions are provided in Chapter 3 of the thesis. In this chapter the so-called mixture conditional autoregressive range (MCARR) model is introduced, examined and applied to daily price ranges of the Hang Seng Index. The conditions for the strict and weak stationarity of the model as well as an expression for the autocorrelation function are obtained by writing the MCARR model as a first order autoregressive process with random coefficients. The chapter also introduces inverse gamma (IG) distribution to CARR models. The advantages of CARR-IG and MCARR-IG specifications over conventional CARR models are found in the empirical application both in- and out-of-sample. Chapter 4 discusses the simultaneous modeling of absolute returns and daily price ranges. In this part of the thesis a vector multiplicative error model (VMEM) with asymmetric Gumbel copula is found to provide substantial benefits over the existing VMEM models based on elliptical copulas. The proposed specification is able to capture the highly asymmetric dependence of the modeled variables thereby improving the performance of the model considerably. The economic significance of the results obtained is established when the information content of the volatility forecasts derived is examined.

Modeling Efficient Classification as a Process of Confidence Assessment and Delegation

In visual object detection and recognition, classifiers have two interesting characteristics: accuracy and speed. Accuracy depends on the complexity of the image features and classifier decision surfaces. Speed depends on the hardware and the computational effort required to use the features and decision surfaces. When attempts to increase accuracy lead to increases in complexity and effort, it is necessary to ask how much are we willing to pay for increased accuracy. For example, if increased computational effort implies quickly diminishing returns in accuracy, then those designing inexpensive surveillance applications cannot aim for maximum accuracy at any cost. It becomes necessary to find trade-offs between accuracy and effort. We study efficient classification of images depicting real-world objects and scenes. Classification is efficient when a classifier can be controlled so that the desired trade-off between accuracy and effort (speed) is achieved and unnecessary computations are avoided on a per input basis. A framework is proposed for understanding and modeling efficient classification of images. Classification is modeled as a tree-like process. In designing the framework, it is important to recognize what is essential and to avoid structures that are narrow in applicability. Earlier frameworks are lacking in this regard. The overall contribution is two-fold. First, the framework is presented, subjected to experiments, and shown to be satisfactory. Second, certain unconventional approaches are experimented with. This allows the separation of the essential from the conventional. To determine if the framework is satisfactory, three categories of questions are identified: trade-off optimization, classifier tree organization, and rules for delegation and confidence modeling. Questions and problems related to each category are addressed and empirical results are presented. For example, related to trade-off optimization, we address the problem of computational bottlenecks that limit the range of trade-offs. We also ask if accuracy versus effort trade-offs can be controlled after training. For another example, regarding classifier tree organization, we first consider the task of organizing a tree in a problem-specific manner. We then ask if problem-specific organization is necessary.

Modeling ecological and evolutionary processes in spatially structured populations

Many species inhabit fragmented landscapes, resulting either from anthropogenic or from natural processes. The ecological and evolutionary dynamics of spatially structured populations are affected by a complex interplay between endogenous and exogenous factors. The metapopulation approach, simplifying the landscape to a discrete set of patches of breeding habitat surrounded by unsuitable matrix, has become a widely applied paradigm for the study of species inhabiting highly fragmented landscapes. In this thesis, I focus on the construction of biologically realistic models and their parameterization with empirical data, with the general objective of understanding how the interactions between individuals and their spatially structured environment affect ecological and evolutionary processes in fragmented landscapes. I study two hierarchically structured model systems, which are the Glanville fritillary butterfly in the Åland Islands, and a system of two interacting aphid species in the Tvärminne archipelago, both being located in South-Western Finland. The interesting and challenging feature of both study systems is that the population dynamics occur over multiple spatial scales that are linked by various processes. My main emphasis is in the development of mathematical and statistical methodologies. For the Glanville fritillary case study, I first build a Bayesian framework for the estimation of death rates and capture probabilities from mark-recapture data, with the novelty of accounting for variation among individuals in capture probabilities and survival. I then characterize the dispersal phase of the butterflies by deriving a mathematical approximation of a diffusion-based movement model applied to a network of patches. I use the movement model as a building block to construct an individual-based evolutionary model for the Glanville fritillary butterfly metapopulation. I parameterize the evolutionary model using a pattern-oriented approach, and use it to study how the landscape structure affects the evolution of dispersal. For the aphid case study, I develop a Bayesian model of hierarchical multi-scale metapopulation dynamics, where the observed extinction and colonization rates are decomposed into intrinsic rates operating specifically at each spatial scale. In summary, I show how analytical approaches, hierarchical Bayesian methods and individual-based simulations can be used individually or in combination to tackle complex problems from many different viewpoints. In particular, hierarchical Bayesian methods provide a useful tool for decomposing ecological complexity into more tractable components.

GABAa Receptor Mediated Signalling in the Brain: Inhibition, Shunting and Excitation

Within central nervous system, the simple division of chemical synaptic transmission to depolarizing excitation mediated by glutamate and hyperpolarizing inhibition mediated by γ-amino butyric acid (GABA), is evidently an oversimplification. The GABAa receptor (GABAaR) mediated responses can be of opposite sign within a single resting cell, due to the compartmentalized distribution of cation chloride cotransporters (CCCs). The K+/Cl- cotransporter 2 (KCC2), member of the CCC family, promotes K+ fuelled Cl- extrusion and sets the reversal potential of GABA evoked anion currents typically slightly below the resting membrane potential. The interesting ionic plasticity property of GABAergic signalling emerges from the short-term and long-term alterations in the intraneuronal concentrations of GABAaR permeable anions (Cl- and HCO3-). The short-term effects arise rapidly (in the time scale of hundreds of milliseconds) and are due to the GABAaR activation dependent shifts in anion gradients, whereas the changes in expression, distribution and kinetic regulation of CCCs are underlying the long-term effects, which may take minutes or even hours to develop. In this Thesis, the differences in the reversal potential of GABAaR mediated responses between dopaminergic and GABAergic cell types, located in the substantia nigra, were shown to be attributable to the differences in the chloride extrusion mechanisms. The stronger inhibitory effect of GABA on GABAergic neurons was due to the cell type specific expression of KCC2 whereas the KCC2 was absent from dopaminergic neurons, leading to a less prominent inhibition brought by GABAaR activation. The levels of KCC2 protein exhibited activity dependent alterations in hippocampal pyramidal neurons. Intense neuronal activity, leading to a massive release of brain derived neurotrophic factor (BDNF) in vivo, or applications of tyrosine receptor kinase B (TrkB) agonists BDNF or neurotrophin-4 in vitro, were shown to down-regulate KCC2 protein levels which led to a reduction in the efficacy of Cl- extrusion. The GABAergic transmission is interestingly involved in an increase of extracellular K+ concentration. A substantial increase in interstitial K+ tends to depolarize the cell membrane. The effects that varying ion gradients had on the generation of biphasic GABAaR mediated responses were addressed, with particular emphasis on the novel idea that the K+/Cl- extrusion via KCC2 is accelerated in response to a rapid accumulation of intracellular Cl-. The KCC2 inhibitor furosemide produced a large reduction in the GABAaR dependent extracellular K+ transients. Thus, paradoxically, both the inefficient KCC2 activity (via increased intracellular Cl-) and efficient KCC2 activity (via increased extracellular K+) may promote excitation.

ORP2 is a sterol receptor that regulates cellular lipid metabolism

ORP2 is a member of mammalian oxysterol binding protein (OSBP)-related protein/gene family (ORPs), which is found in almost every eukaryotic organism. ORPs have been suggested to participate in the regulation of cellular lipid metabolism, vesicle trafficking and cellular signaling. ORP2 is a cytosolic protein that is ubiquitously expressed and most abundant in the brain. In previous studies employing stable cell lines with constitutive ORP2 overexpression ORP2 was shown to affect cellular cholesterol metabolism. The aim of this study was to characterize the properties and function of ORP2 further. ORP2 ligands were searched for among sterols and phosphoinositides using purified ORP2 and in vitro binding assays. As expected, ORP2 bound several oxysterols and cholesterol, the highest affinity ligand being 22(R)hydroxycholesterol. In addition, affinity for anionic membrane phospholipids, phosphoinositides was observed, which may assist in the membrane targeting of ORP2. Intracellular localization of ORP2 was also investigated. ORP2 was observed on the surface of cytoplasmic lipid droplets, which are storage organelles for neutral lipids. Lipid droplet targeting of ORP2 was inhibited when 22(R)hydroxycholesterol was added to the cells or when the N-terminal FFAT-motif of ORP2 was mutated, suggesting that oxysterols and the N-terminus of ORP2 regulate the localization and the function of ORP2. The role of ORP2 in cellular lipid metabolism was studied using HeLa cell lines that can be induced to overexpress ORP2. Overexpression of ORP2 was shown to enhance cholesterol efflux from the cells resulting in a decreased amount of cellular free cholesterol. ORP2 overexpressing cells responded to the loss of cholesterol by upregulating cholesterol synthesis and uptake. Intriguingly, also cholesterol esterification was increased in ORP2 overexpressing cells. These results may be explained by the ability of ORP2 to bind and thus transport cholesterol, which most likely leads to changes in cholesterol metabolism when ORP2 is overexpressed. ORP2 function was further investigated by silencing the endogenous ORP2 expression with short interfering RNAs (siRNA) in A431 cells. Silencing of ORP2 led to a delayed break-down of triglycerides under lipolytic conditions and an increased amount of cholesteryl esters in the presence of excess triglycerides. Together these results suggest that ORP2 is a sterol-regulated protein that functions on the surface of cytoplasmic lipid droplets to regulate the metabolism of triglycerides and cholesteryl esters. Although the exact mode of ORP2 action still remains unclear, this study serves as a good basis to investigate the molecular mechanisms and possible cell type specific functions of ORP2.

Structure and function of GDNF receptor alpha splice variants

The growth factors of the glial cell line-derived neurotrophic factor (GDNF) family consisting of GDNF, neurturin (NRTN), artemin (ARTN) and persephin (PSPN), are involved in the development, differentiation and maintenance of many types of neurons. They also have important functions outside the nervous system in the development of kidney, testis and thyroid gland. Each of these GFLs preferentially binds to one of the glycosylphosphatidylinositol (GPI)-anchored GDNF family receptors α (GFRα). GDNF binds to GFRα1, NRTN to GFRα2, ARTN to GFRα3 and PSPN to GFRα4. The GFLs in the complex with their cognate GFRα receptors all bind to and signal through the receptor tyrosine kinase RET. Alternative splicing of the mouse GFRα4 gene yields three splice isoforms. These had been described as putative GPI-anchored, transmembrane and soluble forms. My goal was to characterise the function of the different forms of mouse GFRα4. I firstly found that the putative GPI-anchored GFRα4 (GFRα4-GPI) is glycosylated, membrane-bound, GPI-anchored and interacts with PSPN and RET. We also showed that mouse GFRα4-GPI mediates PSPN-induced phosphorylation of RET, promotes PSPN-dependent neuronal differentiation of the rat pheochromocytoma cell line PC6-3 and PSPN-dependent survival of cerebellar granule neurons (CGN). However, although this receptor can mediate PSPN-signalling and activate RET, GFRα4-GPI does not recruit RET into lipid rafts. The recruitment of RET into lipid rafts has previously been thought to be a crucial event for GDNF- and GFL-mediated signalling via RET. I secondly demonstrated that the putative transmembrane GFRα4 (GFRα4-TM) is indeed a real transmembrane GFRα4 protein. Although it has a weak binding capacity for PSPN, it can not mediate PSPN-dependent phosphorylation of RET, neuronal differentiation or survival. These data show that GFRα4-TM is inactive as a receptor for PSPN. Surprisingly, GFRα4-TM can negatively regulate PSPN-mediated signalling via GFRα4-GPI. GFRα4-TM interacts with GFRα4-GPI and blocks PSPN-induced phosphorylation of RET, neuronal differentiation as well as survival. Taken together, our data show that GFRα4-TM may act as a dominant negative inhibitor of PSPN-mediated signaling. The most exciting part of my work was the finding that the putative soluble GFRα4 (GFRα4-sol) can form homodimers and function as an agonist of the RET receptor. In the absence of PSPN, GFRα4-sol can promote the phosphorylation of RET, trigger the activation of the PI-3K/AKT pathway, induce neuronal differentiation and support the survival of CGN. Our findings are in line with a recent publication showing the GFRα4-sol might contribute to the inherited cancer syndrome multiple endocrine neoplasia type 2. Our data provide an explanation to how GFRα4-sol may cause or modify the disease. Mammalian GFRα4 receptors all lack the first Cys-rich domain which is present in other GFRα receptors. In the final part of my work I have studied the function of this particular domain. I created a truncated GFRα1 construct lacking the first Cys-rich domain. Using binding assays in both cellular and cell-free systems, phosphorylation assays with RET, as well as neurite outgrowth assays, we found that the first Cys-rich domain contributes to an optimal function of GFRα1, by stabilizing the interaction between GDNF and GFRα1.