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In practice, multivariate dependencies between extreme risks are often only assessed in a pairwise way. We propose a test for detecting situations when such pairwise measures are inadequate and give incomplete results. This occurs when a significant portion of the multivariate dependence structure in the tails is of higher dimension than two. Our test statistic is based on a decomposition of the stable tail dependence function describing multivariate tail dependence. The asymptotic properties of the test are provided and a bootstrap based finite sample version of the test is proposed. A simulation study documents good size and power properties of the test including settings with time-series components and factor models. In an application to stock indices for non-crisis times, pairwise tail models seem appropriate for global markets while the test finds them not admissible for the tightly interconnected European market. From 2007/08 on, however, higher order dependencies generally increase and require a multivariate tail model in all cases.

We propose a framework for estimating network-driven time-varying systemic risk contributions that is applicable to a high-dimensional financial system. Tail risk dependencies and contributions are estimated based on a penalized two-stage fixed-effects quantile approach, which explicitly links bank interconnectedness to systemic risk contributions. The framework is applied to a system of 51 large European banks and 17 sovereigns through the period 2006 to 2013, utilizing both equity and CDS prices. We provide new evidence on how banking sector fragmentation and sovereign-bank linkages evolved over the European sovereign debt crisis and how it is reflected in network statistics and systemic risk measures. Illustrating the usefulness of the framework as a monitoring tool, we provide indication for the fragmentation of the European financial system having peaked and that recovery has started.

We propose a framework for estimating network-driven time-varying systemic risk contributions that is applicable to a high-dimensional financial system. Tail risk dependencies and contributions are estimated based on a penalized two-stage fixed-effects quantile approach, which explicitly links bank interconnectedness to systemic risk contributions. The framework is applied to a system of 51 large European banks and 17 sovereigns through the period 2006 to 2013, utilizing both equity and CDS prices. We provide new evidence on how banking sector fragmentation and sovereign-bank linkages evolved over the European sovereign debt crisis and how it is reflected in network statistics and systemic risk measures. Illustrating the usefulness of the framework as a monitoring tool, we provide indication for the fragmentation of the European financial system having peaked and that recovery has started.

We propose a methodology for forecasting the systemic impact of financial institutions in interconnected systems. Utilizing a five-year sample including the 2008/9 financial crisis, we demonstrate how the approach can be used for timely systemic risk monitoring of large European banks and insurance companies. We predict firms’ systemic relevance as the marginal impact of individual downside risks on systemic distress. The so-called systemic risk betas account for a company’s position within the network of financial interdependencies in addition to its balance sheet characteristics and its exposure towards general market conditions. Relying only on publicly available daily market data, we determine time-varying systemic risk networks, and forecast systemic relevance on a quarterly basis. Our empirical findings reveal time-varying risk channels and firms’ specific roles as risk transmitters and/or risk recipients.

We propose the realized systemic risk beta as a measure for financial companies' contribution to systemic risk given network interdependence between firms' tail risk exposures. Conditional on statistically pre-identified network spillover effects and market and balance sheet information, we define the realized systemic risk beta as the total time-varying marginal effect of a firm's Value-at-risk (VaR) on the system's VaR. Suitable statistical inference reveals a multitude of relevant risk spillover channels and determines companies' systemic importance in the U.S. financial system. Our approach can be used to monitor companies' systemic importance allowing for a transparent macroprudential regulation.

Standard fixed symmetric kernel type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. We show that in such settings, alternatives of asymmetric gamma kernel estimators are superior but also differ in asymptotic and finite sample performance conditional on the shape of the density near zero and the exact form of the chosen kernel. We therefore suggest a refined version of the gamma kernel with an additional tuning parameter according to the shape of the density close to the boundary. We also provide a data-driven method for the appropriate choice of the modified gamma kernel estimator. In an extensive simulation study we compare the performance of this refined estimator to standard gamma kernel estimates and standard boundary corrected and adjusted fixed kernels. We find that the finite sample performance of the proposed new estimator is superior in all settings. Two empirical applications based on high-frequency stock trading volumes and realized volatility forecasts demonstrate the usefulness of the proposed methodology in practice.

We give an overview over smooth backfitting type estimators in additive models. Moreover we illustrate their wide applicability in models closely related to additive models such as nonparametric regression with dependent error variables where the errors can be transformed to white noise by a linear transformation, nonparametric regression with repeatedly measured data, nonparametric panels with fixed effects, simultaneous nonparametric equation models, and non- and semiparamet- ric autoregression and GARCH-models. We also discuss extensions to varying coeficient models, additive models with missing observations, and the case of nonstationary covariates.

In many applications, covariates are not observed but have to be estimated from data. We outline some regression-type models where such a situation occurs and discuss estimation of the regression function in this context.We review theoretical results on how asymptotic properties of nonparametric estimators differ in the presence of generated covariates from the standard case where all covariates are observed. These results also extend to settings where the focus of interest is on average functionals of the regression function.

In many applications, covariates are not observed but have to be estimated from data. We outline some regression-type models where such a situation occurs and discuss estimation of the regression function in this context.We review theoretical results on how asymptotic properties of nonparametric estimators differ in the presence of generated covariates from the standard case where all covariates are observed. These results also extend to settings where the focus of interest is on average functionals of the regression function.

We give an overview over smooth back tting type estimators in additive models. Moreover we illustrate their wide applicability in models closely related to additive models such as nonparametric regression with dependent error variables where the errors can be transformed to white noise by a linear transformation, nonparametric regression with repeatedly measured data, nonparametric panels with fixed effects, simultaneous nonparametric equation models, and non- and semiparametric autoregression and GARCH-models. We also discuss extensions to varying coeffcient models, additive models with missing observations, and the case of nonstationary covariates.

This article studies nonparametric estimation of a regression model for d ≥ 2 potentially non- stationary regressors. It provides the first nonparametric procedure for a wide and important range of practical problems, for which there has been no applicable nonparametric estimation technique before. Additive regression allows to circumvent the usual nonparametric curse of dimensionality and the additionally present, nonstationary curse of dimensionality while still pertaining high mod- eling flexibility. Estimation of an additive conditional mean function can be conducted under weak conditions: It is sufficient that the response Y and all univariate Xj and pairs of bivariate marginal components Xjk of the vector of all covariates X are (potentially nonstationary) β-null Harris re- current processes. The full dimensional vector of regressors X itself, however, is not required to be Harris recurrent. This is particularly important since e.g. random walks are Harris recurrent only up to dimension two. Under different types of independence assumptions, asymptotic distributions are derived for the general case of a (potentially nonstationary) β-null Harris recurrent noise term ε but also for the special case of ε being stationary mixing. The later case deserves special attention since the model might be regarded as an additive type of cointegration model. In contrast to existing more general approaches, the number of cointegrated regressors is not restricted. Finite sample properties are illustrated in a simulation study.

We propose the realized systemic risk beta as a measure for financial companies’ contribution to systemic risk given network interdependence between firms’ tail risk exposures. Conditional on statistically pre-identified network spillover effects and market and balance sheet information, we define the realized systemic risk beta as the total time-varying marginal effect of a firm’s Value-at-risk (VaR) on the system’s VaR. Suitable statistical inference reveals a multitude of relevant risk spillover channels and determines companies’ systemic importance in the U.S. financial system. Our approach can be used to monitor companies’ systemic importance allowing for a transparent macroprudential regulation.

In this paper, we study a general class of semiparametric optimization estimators of a vector-valued parameter. The criterion function depends on two types of in nite-dimensional nuisance parameters: a conditional expectation function that has been estimated nonparametrically using generated covariates, and another estimated function that is used to compute the generated covariates in the first place. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root-n consistent and asymptotically normal, and derive a general formula for the asymptotic variance.

We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed on high frequencies, such as cumulated trading volumes or the time between potentially simultaneously occurring market events. We introduce a flexible pointmass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model (MEM) based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of liquid NYSE stocks, we show that the model captures both the dynamic and distribution properties of the data very well and is able to correctly predict future distributions. Keywords: High-frequency Data , Point-mass Mixture , Multiplicative Error Model , Excess Zeros , Semiparametric Specification Test , Market Microstructure JEL Classification: C22, C25, C14, C16, C51

We propose a novel approach to model serially dependent positive-valued variables which realize a non-trivial proportion of zero outcomes. This is a typical phenomenon in financial time series observed on high frequencies, such as cumulated trading volumes or the time between potentially simultaneously occurring market events. We introduce a flexible point-mass mixture distribution and develop a semiparametric specification test explicitly tailored for such distributions. Moreover, we propose a new type of multiplicative error model (MEM) based on a zero-augmented distribution, which incorporates an autoregressive binary choice component and thus captures the (potentially different) dynamics of both zero occurrences and of strictly positive realizations. Applying the proposed model to high-frequency cumulated trading volumes of liquid NYSE stocks, we show that the model captures both the dynamic and distribution properties of the data very well and is able to correctly predict future distributions.

This chapter deals with nonparametric estimation of the risk neutral density. We present three different approaches which do not require parametric functional assumptions on the underlying asset price dynamics nor on the distributional form of the risk neutral density. The first estimator is a kernel smoother of the second derivative of call prices, while the second procedure applies kernel type smoothing in the implied volatility domain. In the conceptually different third approach we assume the existence of a stochastic discount factor (pricing kernel) which establishes the risk neutral density conditional on the physical measure of the underlying asset. Via direct series type estimation of the pricing kernel we can derive an estimate of the risk neutral density by solving a constrained optimization problem. The methods are compared using European call option prices. The focus of the presentation is on practical aspects such as appropriate choice of smoothing parameters in order to facilitate the application of the techniques.

This thesis studies nonparametric estimation techniques for a general regression set–up under very weak conditions on the covariate process. In particular, regressors are allowed to be high–dimensional stochastically nonstationary processes. The concept of nonstationarity comprises time series observations of random walk or long memory type. Admissible processes are ß–null Harris recurrent processes. We introduce the first kernel type estimation method for such nonstationary regressors without restricting their dimension. This set–up is motivated by and generalizes approaches in parametric econometric time series analysis with nonstationary components. Additive regression allows to circumvent the usual nonparametric curse of dimensionality and to countervail the additionally present, nonstationary curse of dimensionality while still pertaining high modeling flexibility. We propose a backfitting type estimation procedure where it is sufficient that the response Y and all univariate Xj and pairs of bivariate marginal components Xjk of the vector of all covariates X are (potentially nonstationary) ß–null Harris recurrent processes. The full dimensional vector of regressors X itself, however, is not required to be Harris recurrent. This is particularly important since e.g. random walks are Harris recurrent only up to dimension two. Though we also suggest tailored estimation methods if more than two covariates are ß–null Harris recurrent, which can provide the best additive fit in a projection sense to a more general non-additive class of true models. Under different types of independence assumptions, asymptotic distributions are derived for the general case of a (potentially nonstationary) ß-null Harris recurrent residual but also for the special case of the residual being stationary mixing. The later case deserves special attention, since the model might be regarded as an additive type of cointegration model. In contrast to existing more general approaches, the number of cointegrated regressors is not restricted. In general, we need no pre-testing for stationary or nonstationary covariates, the same method applies to all. Though if we have pre-information that some covariates are stationary and we know which ones, we present a tailored estimation procedure which allows to obtain faster rates of convergence fully countervailing the nonstationary curse of dimensionality. In particular, we manage to estimate stationary components at stationary rates which confirms the practical relevance of the procedure. Furthermore finite sample properties are discussed in a simulation study.

In an increasingly digital world, data has become abundant and research about leveraging such vast amounts of data is on the rise. While extracting important information relevant for economic policies or financial risk is crucial, the often non-standard structure of such observational data poses many challenges for researchers. That includes highly correlated, time-dependent data, combinations of unstructured data, and even high-dimensional situations, where we have very few data points and many potentially relevant factors. In this thesis, I tackle the above challenges by developing interpretable statistical machine learning methods to reveal important effects of public policies, to better assess risks in financial applications, and to quantify market drivers. I study causal inference, statistical model selection, and prediction in different social and economic contexts in order to uncover statistical relationships and to identify important contributing factors. In the first part of my work, I analyze financial risk with cryptocurrencies and corporate bonds. For the former, I identify classes of assets and time periods where flexible machine learning methods, such as random forests employed within a statistical framework, significantly improve predictability of risk. This is vital given the highly volatile return structure of cryptocurrencies. For corporate bonds, I uncover drivers of the risk of default by developing a method that correctly handles the underlying, highly correlated, time series data. In the second part, I focus on the evaluation of the causal effect of tuition fees on university student enrollment. I develop methods to deal with the many possible influencing factors given only few observations by combining subsampling-based methods with regularization in a panel setup. I can show that there was a causal effect of the short tuition fee period in Germany by disentangling this effect from other factors and policies. In the third part, I combine satellite images with many noisy, observational data sources to show the impact of crime on the housing market of New York City on a spatial grid. To overcome the endogeneity of crime for house prices, I develop a method that leverages satellite data, can be easily extended to other cities, and highlights the non-linearity of crime on a spatial level.

Das moderne Finanzsystem ist komplex, dynamisch, hochdimensional und oftmals nicht stationär. All diese Faktoren stellen große Herausforderungen beim Messen des zugrundeliegenden Finanzrisikos dar, das speziell für Marktteilnehmer von oberster Priorität ist. Hochdimensionalität, die aus der ansteigenden Vielfalt an Finanzprodukten entsteht, ist ein wichtiges Thema für Ökonometriker. Ein Standardansatz, um mit hoher Dimensionalität umzugehen, ist es, Schlüsselvariablen auszuwählen und kleine Koeffizientenen auf null zu setzen, wie etwa Lasso. In der Finanzmarktanalyse kann eine solche geringe Annahme helfen, die führenden Risikofaktoren aus dem extrem großen Portfolio, das letztendlich das robuste Maß für finanzielles Risiko darstellt, hervorzuheben. In dieser Arbeit nutzen wir penalisierte Verfahren, um die ökonometrischen Maße für das finanzielle Risiko in hoher Dimension zu schätzen, sowohl mit nieder-, als auch hochfrequenten Daten. Mit Fokus auf dem Finanzmarkt, können wir das Risikonetzwerk des ganzen Systems konstruieren, das die Identifizierung individualspezifischen Risikos erlaubt. Modern financial system is complex, dynamic, high-dimensional and often possibly non-stationary. All these factors pose great challenges in measuring the underlying financial risk, which is of top priority especially for market participants. High-dimensionality, which arises from the increasing variety of the financial products, is an important issue among econometricians. A standard approach dealing with high dimensionality is to select key variables and set small coefficient to zero, such as lasso. In financial market analysis, such sparsity assumption can help highlight the leading risk factors from the extremely large portfolio, which constitutes the robust measure for financial risk in the end. In this paper we use penalized techniques to estimate the econometric measures of financial risk in high dimensional, with both low-frequency and high-frequency data. With focus on financial market, we could construct the risk network of the whole system which allows for identification of individual-specific risk.

Diese Dissertation behandelt die ökonometrische Analyse von hochfrequenten Finanzmarktdaten. Kapitel 1 stellt einen neuen Ansatz zur Modellierung von seriell abhängigen positiven Variablen, die einen nichttrivialen Anteil an Nullwerten aufweisen, vor. Letzteres ist ein weitverbreitetes Phänomen in hochfrequenten Finanzmarktzeitreihen. Eingeführt wird eine flexible Punktmassenmischverteilung, ein maßgeschneiderter semiparametrischer Spezifikationstest sowie eine neue Art von multiplikativem Fehlermodell (MEM). Kapitel 2 beschäftigt sich mit dem Umstand, dass feste symmetrische Kerndichteschätzer eine geringe Präzision aufweisen, falls eine positive Zufallsvariable mit erheblicher Wahrscheinlichkeitsmasse nahe Null gegeben ist. Wir legen dar, dass Gammakernschätzer überlegen sind, wobei ihre relative Präzision von der genauen Form der Dichte sowie des Kerns abhängt. Wir führen einen verbesserten Gammakernschätzer sowie eine datengetriebene Methodik für die Wahl des geeigneten Typs von Gammakern ein. Kapitel 3 wendet sich der Frage nach dem Nutzen von Hochfrequenzdaten für hochdimensionale Portfolioallokationsanwendungen zu. Wir betrachten das Problem der Konstruktion von globalen Minimum-Varianz-Portfolios auf der Grundlage der Konstituenten des S&P 500. Wir zeigen auf, dass Prognosen, welche auf Hochfrequenzdaten basieren, im Vergleich zu Methoden, die tägliche Renditen verwenden, eine signifikant geringere Portfoliovolatilität implizieren. Letzteres geht mit spürbaren Nutzengewinnen aus der Sicht eines Investors mit hoher Risikoaversion einher. In three essays, this thesis deals with the econometric analysis of financial market data sampled at intraday frequencies. Chapter 1 presents a novel approach to model serially dependent positive-valued variables realizing a nontrivial proportion of zero outcomes. This is a typical phenomenon in financial high-frequency time series. We introduce a flexible point-mass mixture distribution, a tailor-made semiparametric specification test and a new type of multiplicative error model (MEM). Chapter 2 addresses the problem that fixed symmetric kernel density estimators exhibit low precision for positive-valued variables with a large probability mass near zero, which is common in high-frequency data. We show that gamma kernel estimators are superior, while their relative performance depends on the specific density and kernel shape. We suggest a refined gamma kernel and a data-driven method for choosing the appropriate type of gamma kernel estimator. Chapter 3 turns to the debate about the merits of high-frequency data in large-scale portfolio allocation. We consider the problem of constructing global minimum variance portfolios based on the constituents of the S&P 500. We show that forecasts based on high-frequency data can yield a significantly lower portfolio volatility than approaches using daily returns, implying noticeable utility gains for a risk-averse investor.

In dieser Dissertation werden neue Methoden zur Erfassung zweier Risikoarten entwickelt. Markrisiko ist definiert als das Risiko, auf Grund von Wertrückgängen in Wertpapierportfolios Geld zu verlieren. Systemisches Risiko bezieht sich auf das Risiko des Zusammenbruchs eines Finanzsystems, das durch die Notlage eines einzelnen Finanzinstituts entsteht. Im Zuge der Finanzkrise 2007–2009 realisierten sich beide Risiken, was weltweit zu hohen Verlusten für Investoren, Unternehmen und Steuerzahler führte. Vor diesem Hintergrund besteht sowohl bei Finanzinstituten als auch bei Regulierungsbehörden Interesse an neuen Ansätzen für das Risikomanagement. Die Gemeinsamkeit der in dieser Dissertation entwickelten Methoden besteht darin, dass unterschiedliche Quantilsregressionsansätze in neuartiger Weise für das Finanzrisikomanagement verwendet werden. Zum einen wird nichtparametrische Quantilsregression mit Extremwertmethoden kombiniert, um extreme Markpreisänderungsrisiken zu prognostizieren. Das resultierende Value at Risk (VaR) Prognose- Modell für extremeWahrscheinlichkeiten wird auf internationale Aktienindizes angewandt. In vielen Fällen schneidet es besser ab als parametrische Vergleichsmodelle. Zum anderen wird ein Maß für systemisches Risiko, das realized systemic risk beta, eingeführt. Anders als bereits existierende Messgrößen erfasst es explizit sowohl Risikoabhängigkeiten zwischen Finanzinstituten als auch deren individuelle Bilanzmerkmale und Finanzsektor-Indikatoren. Um die relevanten Risikotreiber jedes einzelnen Unternehmens zu bestimmen, werden Modellselektionsverfahren für hochdimensionale Quantilsregressionen benutzt. Das realized systemic risk beta entspricht dem totalen Effekt eines Anstiegs des VaR eines Unternehmens auf den VaR des Finanzsystems. Anhand von us-amerikanischen und europäischen Daten wird gezeigt, dass die neue Messzahl sich gut zur Erfassung und Vorhersage systemischen Risikos eignet. This thesis develops new methods to assess two types of financial risk. Market risk is defined as the risk of losing money due to drops in the values of asset portfolios. Systemic risk refers to the breakdown risk for the financial system induced by the distress of individual companies. During the financial crisis 2007–2009, both types of risk materialized, resulting in huge losses for investors, companies, and tax payers all over the world. Therefore, considering new risk management alternatives is of interest for both financial institutions and regulatory authorities. A common feature of the models used throughout the thesis is that they adapt quantile regression techniques to the context of financial risk management in a novel way. Firstly, to predict extreme market risk, nonparametric quantile regression is combined with extreme value theory. The resulting extreme Value at Risk (VaR) forecast framework is applied to different international stock indices. In many situations, its performance is superior to parametric benchmark models. Secondly, a systemic risk measure, the realized systemic risk beta, is proposed. In contrast to exististing measures it is tailored to account for tail risk interconnections within the financial sector, individual firm characteristics, and financial indicators. To determine each company’s relevant risk drivers, model selection techniques for high-dimensional quantile regression are employed. The realized systemic risk beta corresponds to the total effect of each firm’s VaR on the system’s VaR. Using data on major financial institutions in the U.S. and in Europe, it is shown that the new measure is a valuable tool to both estimate and forecast systemic risk.