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.

Evidence for u.v. induction of CDKN2 mutations in melanoma cell lines

The CDKN2 gene, encoding the cyclin dependent kinase inhibitor p16, is a tumour suppressor gene involved in melanoma and maps to chromosome band 9p22. Mutations or interstitial deletions of this gene have been found both in the germline of familial melanoma cases and somatically in melanoma cell lines. Previous mutation analyses of melanoma cell lines have indicated a high frequency of C:G to T:A transitions, with all of these mutations occurring at dipyrimidine sites. Including three melanoma cell lines carrying tandem CC to TT mutations, the spectrum of mutations so far reported indicates a possible role for u.v. radiation in the mutagenesis of this gene in some tumours. To further examine this hypothesis we have characterised mutations of the CDKN2 gene in 30 melanoma cell lines. Nineteen lines carried complete or partial homozygous deletions of the gene. Of the remaining cell lines, eight were shown by direct sequencing of PCR products from exon 1 and exon 2 to carry a total of nine different mutations of CDKN2. Two cell lines carried tandem CC to TT mutations and a high rate of C:G to T:A transitions was observed. This study provides further evidence for the role of u.v. light in the genesis of melanoma, with one target being the CDKN2 tumour suppressor gene.

CDKN2A/p16 is inactivated in most melanoma cell lines

The CDKN2A gene maps to chromosome 9p21-22 and is responsible for melanoma susceptibility in some families. Its product, p16, binds specifically to CDK4 and CDK6 in vitro and in vivo, inhibiting their kinase activity. CDKN2A is homozygously deleted or mutated in a large proportion of tumor cell lines and some primary tumors, including melanomas. The aim of this study was to investigate the involvement of CDKN2A and elucidate the mechanisms of p16 inactivation in a panel of 60 cell lines derived from sporadic melanomas. Twenty-six (43%) of the melanoma lines were homozygously deleted for CDKN2A, and an additional 15 (25%) lines carried missense, nonsense, or frameshift mutations. All but one of the latter group were shown by microsatellite analysis to be hemizygous for the region of 9p surrounding CDKN2A. p16 was detected by Western blotting in only five of the cell lines carrying mutations. Immunoprecipitation of p16 in these lines, followed by Western blotting to detect the coprecipitation of CDK4 and CDK6, revealed that p16 was functionally compromised in all cell lines but the one that carried a heterozygous CDKN2A mutation. In the remaining 19 lines that carried wild-type CDKN2A alleles, Western blot analysis and immunoprecipitation indicated that 11 cell lines expressed a wild-type protein. Northern blotting was performed on the remaining eight cell lines and revealed that one cell line carried an aberrantly sized RNA transcript, and two other cell lines failed to express RNA. The promoter was found to be methylated in five cell lines that expressed CDKN2A transcript but not p16. Presumably, the message seen by Northern blotting in these cell lines is the result of cross-hybridization of the total cDNA probe with the exon 1beta transcript. Microsatellite analysis revealed that the majority of these cell lines were hemi/homozygous for the region surrounding CDKN2A, indicating that the wild-type allele had been lost. In the 11 cell lines that expressed functional p16, microsatellite analysis revealed loss of heterozygosity at the markers immediately surrounding CDKN2A in five cases, and the previously characterized R24C mutation of CDK4 was identified in one of the remaining 6 lines. These data indicate that 55 of 60 (92%) melanoma cell lines demonstrated some aberration of CDKN2A or CDK4, thus suggesting that this pathway is a primary genetic target in melanoma development.

CDKN2A is not the principal target of deletions on the short arm of chromosome 9 in neuroendocrine (Merkel cell) carcinoma of the skin

The majority of small-cell lung cancers (SCLCs) express p16 but not pRb. Given our previous study showing loss of pRb in Merkel cell carcinoma (MCC)/neuroendocrine carcinoma of the skin and the clinicopathological similarities between SCLC and MCC, we wished to determine if this was also the case in MCC. Twenty-nine MCC specimens from 23 patients were examined for deletions at 10 loci on 9p and 1 on 9q. No loss of heterozygosity (LOH) was seen in 9 patients including 2 for which tumour and cell line DNAs were examined. Four patients had LOH for all informative loci on 9p. Ten tumours showed more limited regions of loss on 9p, and from these 2 common regions of deletion were determined. Half of all informative cases had LOH at D9S168, the most telomeric marker examined, and 3 specimens showed loss of only D9S168. A second region (IFNA-D9S126) showed LOH in 10 (44%) cases, and case MCC26 showed LOH for only D9S126, implicating genes centromeric of the CDKN2A locus. No mutations in the coding regions of p16 were seen in 7 cell lines tested, and reactivity to anti-p16 antibody was seen in all 11 tumour specimens examined and in 6 of 7 cell lines from 6 patients. Furthermore, all cell lines examined reacted with anti-p14(ARF) antibody. These results suggest that neither transcript of the CDKN2A locus is the target of deletions on 9p in MCC and imply the existence of tumour-suppressor genes mapping both centromeric and telomeric of this locus.

Mutations in exon 3 of the beta-catenin gene are rare in melanoma cell lines

Mutations in exon 3 of the CTNNB1 gene encoding beta-catenin have been reported in colorectal cancer cell lines and tumours. Although one study reported mutations or deletions affecting beta-catenin in 20% of melanoma cell lines, subsequent reports detected a much lower frequency of aberrations in uncultured melanomas. To determine whether this difference in mutation frequency reflected an in vitro culturing artefact, exon 3 of CTNNB1 was screened in a panel of 62 melanoma cell lines. In addition, reverse transcription-polymerase chain reaction (RT-PCR) was performed to detect intragenic deletions affecting exon 3. One out of 62 (1.6%) cell lines was found to carry a mutation, indicating that aberration of the Wnt-1/wingless pathway through activation of beta-catenin is a rare event, even in melanoma cell lines.

PTEN inactivation is rare in melanoma tumours but occurs frequently in melanoma cell lines

Deletions detected in cytogenetic and loss of heterozygosity (LOH) studies indicate that at least one tumour suppressor gene maps to the long arm of chromosome 10. Previous deletion mapping studies have observed LOH on 10q in about 30% of melanomas analysed. The PTEN gene, mapping to chromosome band 10q23.3, encodes a protein with both lipid and protein phosphatase activity. Somatic mutations and deletions in have been detected in a variety of cell lines and tumours, including melanoma samples. We performed mutation analyses and extensive allelic loss studies to investigate the role this gene plays in melanoma pathogenesis. We found that a total of 34 out of 57 (60%) melanoma cell lines carried hemizygous deletions of chromosome 10q encompassing the PTEN locus. A further three cell lines carried smaller deletions excluding PTEN. Inactivation of both PTEN alleles by exon-specific homozygous deletion or mutation was observed in 13 out of 57 (23%) melanoma cell lines. The mutation spectrum observed does not indicate an important role for ultraviolet radiation in the genesis of these mutations, and evidence from three cell lines supports the acquisition of PTEN aberrations in culture. Ten out of 49 (20%) matched melanoma tumour/normal samples harboured hemizygous deletions of either the whole chromosome or most of the long arm. Mutations within were detected in only one of the 10 tumours demonstrating LOH at 10q23 that were analysed. These results suggest that PTEN inactivation may be important for the propagation of melanoma cells in culture, and that another chromosome 10 tumour suppressor gene may be important for melanoma pathogenesis.

p53 prevents progression of nevi to melanoma predominantly through cell cycle regulation

p53 is the central member of a critical tumor suppressor pathway in virtually all tumor types, where it is silenced mainly by missense mutations. In melanoma, p53 predominantly remains wild type, thus its role has been neglected. To study the effect of p53 on melanocyte function and melanomagenesis, we crossed the 'high-p53'Mdm4+/- mouse to the well-established TP-ras0/+ murine melanoma progression model. After treatment with the carcinogen dimethylbenzanthracene (DMBA), TP-ras0/+ mice on the Mdm4+/- background developed fewer tumors with a delay in the age of onset of melanomas compared to TP-ras0/+ mice. Furthermore, we observed a dramatic decrease in tumor growth, lack of metastasis with increased survival of TP-ras0/+: Mdm4+/- mice. Thus, p53 effectively prevented the conversion of small benign tumors to malignant and metastatic melanoma. p53 activation in cultured primary melanocyte and melanoma cell lines using Nutlin-3, a specific Mdm2 antagonist, supported these findings. Moreover, global gene expression and network analysis of Nutlin-3-treated primary human melanocytes indicated that cell cycle regulation through the p21WAF1/CIP1 signaling network may be the key anti-melanomagenic activity of p53.

Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Stochastic simulation for spatial modelling of dynamic process in a living cell

One of the fundamental motivations underlying computational cell biology is to gain insight into the complicated dynamical processes taking place, for example, on the plasma membrane or in the cytosol of a cell. These processes are often so complicated that purely temporal mathematical models cannot adequately capture the complex chemical kinetics and transport processes of, for example, proteins or vesicles. On the other hand, spatial models such as Monte Carlo approaches can have very large computational overheads. This chapter gives an overview of the state of the art in the development of stochastic simulation techniques for the spatial modelling of dynamic processes in a living cell.

Phenomenological modeling of cell-to-cell and beat-to-beat variability in isolated Guinea Pig ventricular myocytes

Experimental action potential (AP) recordings in isolated ventricular myoctes display significant temporal beat-to-beat variability in morphology and duration. Furthermore, significant cell-to-cell differences in AP also exist even for isolated cells originating from the same region of the same heart. However, current mathematical models of ventricular AP fail to replicate the temporal and cell-to-cell variability in AP observed experimentally. In this study, we propose a novel mathematical framework for the development of phenomenological AP models capable of capturing cell-to-cell and temporal variabilty in cardiac APs. A novel stochastic phenomenological model of the AP is developed, based on the deterministic Bueno-Orovio/Fentonmodel. Experimental recordings of AP are fit to the model to produce AP models of individual cells from the apex and the base of the guinea-pig ventricles. Our results show that the phenomenological model is able to capture the considerable differences in AP recorded from isolated cells originating from the location. We demonstrate the closeness of fit to the available experimental data which may be achieved using a phenomenological model, and also demonstrate the ability of the stochastic form of the model to capture the observed beat-to-beat variablity in action potential duration.

An ultraviolet selective photodetector based on a nanocrystalline TiO2 photoelectrochemical cell

Solar ultraviolet (UV) radiation causes a range of skin disorders as well as affecting vision and the immune system. It also inhibits development of plants and animals. UV radiation monitoring is used routinely in some locations in order to alert the population to harmful solar radiation levels. There is ongoing research to develop UV-selective-sensors [1–3]. A personal, inexpensive and simple UV-selective-sensor would be desirable to measure UV intensity exposure. A prototype of such a detector has been developed and evaluated in our laboratory. It comprises a sealed two-electrode photoelectrochemical cell (PEC) based on nanocrystalline TiO2. This abundant semiconducting oxide, which is innocuous and very sta-ble, is the subject of intense study at present due to its application in dye sensitized solar cells (DSSC) [4]. Since TiO2 has a wide band gap (EG = 3.0 eV for rutile and EG = 3.2 eV for anatase), it is inher-ently UV-selective, so that UV filters are not required. This further reduces the cost of the proposed photodetector in comparison with conventional silicon detectors. The PEC is a semiconductor–electrolyte device that generates a photovoltage when it is illuminated and a corresponding photocur-rent if the external circuit is closed. The device does not require external bias, and the short circuit current is generally a linear function of illumination intensity. This greatly simplifies the elec-trical circuit needed when using the PEC as a photodetector. DSSC technology, which is based on a PEC containing nanocrystalline TiO2 sensitized with a ruthenium dye, holds out the promise of solar cells that are significantly cheaper than traditional silicon solar cells. The UV-sensor proposed in this paper relies on the cre-ation of electron–hole pairs in the TiO2 by UV radiation, so that it would be even cheaper than a DSSC since no sensitizer dye is needed. Although TiO2 has been reported as a suitable material for UV sensing [3], to the best of our knowledge, the PEC configuration described in the present paper is a new approach. In the present study, a novel double-layer TiO2 structure has been investigated. Fabrication is based on a simple and inexpensive technique for nanostructured TiO2 deposition using microwave-activated chemical bath deposition (MW-CBD) that has been reported recently [5]. The highly transparent TiO2 (anatase) films obtained are densely packed, and they adhere very well to the transparent oxide (TCO) substrate [6]. These compact layers have been studied as contacting layers in double-layer TiO2 structures for DSSC since improvement of electron extraction at the TiO2–TCO interface is expected [7]. Here we compare devices incorporating a single mesoporous nanocrystalline TiO2 structure with devices based on a double structure in which a MW-CBD film is situated between the TCO and the mesoporous nanocrystalline TiO2 layer. Besides improving electron extraction, this film could also help to block recombination of electrons transferred to the TCO with oxidized species in the electrolyte, as has been reported in the case of DSSC for compact TiO2 films obtained by other deposition tech-niques [8,9]. The two types of UV-selective sensors were characterized in detail. The current voltage characteristics, spectral response, inten-sity dependence of short circuit current and response times were measured and analyzed in order to evaluate the potential of sealed mesoporous TiO2-based photoelectrochemical cells (PEC) as low cost personal UV-photodetectors.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.