Shortcomings of a parametric VaR approach and nonparametric improvements based on a non-stationary return series model

A non-stationary regression model for financial returns is examined theoretically in this paper. Volatility dynamics are modelled both exogenously and deterministic, captured by a nonparametric curve estimation on equidistant centered returns. We prove consistency and asymptotic normality of a symmetric variance estimator and of a one-sided variance estimator analytically, and derive remarks on the bandwidth decision. Further attention is paid to asymmetry and heavy tails of the return distribution, implemented by an asymmetric version of the Pearson type VII distribution for random innovations. By providing a method of moments for its parameter estimation and a connection to the Student-t distribution we offer the framework for a factor-based VaR approach. The approximation quality of the non-stationary model is supported by simulation studies. --heteroscedastic asset returns,non-stationarity,nonparametric regression,volatility,innovation modelling,asymmetric heavy-tails,distributional forecast,Value at Risk (VaR)

Financial Risk Measurement for Financial Risk Management

Current practice largely follows restrictive approaches to market risk measurement, such as historical simulation or RiskMetrics. In contrast, we propose flexible methods that exploit recent developments in financial econometrics and are likely to produce more accurate risk assessments, treating both portfolio-level and asset-level analysis. Asset-level analysis is particularly challenging because the demands of real-world risk management in financial institutions - in particular, real-time risk tracking in very high-dimensional situations - impose strict limits on model complexity. Hence we stress powerful yet parsimonious models that are easily estimated. In addition, we emphasize the need for deeper understanding of the links between market risk and macroeconomic fundamentals, focusing primarily on links among equity return volatilities, real growth, and real growth volatilities. Throughout, we strive not only to deepen our scientific understanding of market risk, but also cross-fertilize the academic and practitioner communities, promoting improved market risk measurement technologies that draw on the best of both.Market risk, volatility, GARCH

Statistical modelling of algorithms for signal processing in systems based on environment perception

One cornerstone for realising automated driving systems is an appropriate handling of uncertainties in the environment perception and situation interpretation. Uncertainties arise due to noisy sensor measurements or the unknown future evolution of a traffic situation. This work contributes to the understanding of these uncertainties by modelling and propagating them with parametric probability distributions

Robust Computational Tools for Multiple Testing with Genetic Association Studies

Resolving the interplay of the genetic components of a complex disease is a challenging endeavor. Over the past several years, genome-wide association studies (GWAS) have emerged as a popular approach at locating common genetic variation within the human genome associated with disease risk. Assessing genetic-phenotype associations upon hundreds of thousands of genetic markers using the GWAS approach, introduces the potentially high number of false positive signals and requires statistical correction for multiple hypothesis testing. Permutation tests are considered the gold standard for multiple testing correction in GWAS, because they simultaneously provide unbiased Type I error control and high power. However, they demand heavy computational effort, especially with large-scale data sets of modern GWAS. In recent years, the computational problem has been circumvented by using approximations to permutation tests, but several studies have posed sampling conditions in which these approximations are suggestive to be biased. We have developed an optimized parallel algorithm for the permutation testing approach to multiple testing correction in GWAS, whose implementation essentially abates the computational problem. When introduced to GWAS data, our algorithm yields rapid, precise, and powerful multiplicity adjustment, many orders of magnitude faster than existing employed GWAS statistical software. Although GWAS have identified many potentially important genetic associations which will advance our understanding of human disease, the common variants with modest effects on disease risk discovered through this approach likely account for a small proportion of the heritability in complex disease. On the other hand, interactions between genetic and environmental factors could account for a substantial proportion of the heritability in a complex disease and are overlooked within the GWAS approach. We have developed an efficient and easily implemented tool for genetic association studies, whose aim is identifying genes involved in a gene-environment interaction. Our approach is amenable to a wide range of association studies and assorted densities in sampled genetic marker panels, and incorporates resampling for multiple testing correction. Within the context of a case-control study design we demonstrate by way of simulation that our proposed method offers greater statistical power to detect gene-environment interaction, when compared to several competing approaches to assess this type of interaction