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This paper develops a novel method for policy choice in a dynamic setting where the available data is a multi-variate time-series. Building on the statistical treatment choice framework, we propose Time-series Empirical Welfare Maximization (T-EWM) methods to estimate an optimal policy rule for the current period or over multiple periods by maximizing an empirical welfare criterion constructed using nonparametric potential outcome time-series. We characterize conditions under which T-EWM consistently learns a policy choice that is optimal in terms of conditional welfare given the time-series history. We then derive a nonasymptotic upper bound for conditional welfare regret and its minimax lower bound. To illustrate the implementation and uses of T-EWM, we perform simulation studies and apply the method to estimate optimal monetary policy rules from macroeconomic time-series data.

A factor augmented dynamic model for analysing tail behaviour of high dimensional time series is proposed. As a first step, the tail event driven latent factors are extracted. In the second step, a VAR (Vectorautoregression model) is carried out to analyse the interaction between these factors and the macroeconomic variables. Furthermore, this methodology also provides the possibility for central banks to examine the sensitivity between macroeconomic variables and financial shocks via impulse response analysis. Then the predictability of our estimator is illustrated. Finally, forecast error variance decomposition is carried out to investigate the network effect of these variables. The interesting findings are: firstly, GDP and Unemployment rate are very much sensitive to the shock of financial tail event driven factors, while these factors are more affected by inflation and short term interest rate. Secondly, financial tail event driven factors play important roles in the network constructed by the extracted factors and the macroeconomic variables. Thirdly, there is more connectedness during financial crisis than in the stable periods. Compared with median case, the network is more dense in lower quantile level.

In this paper, we study estimation of nonlinear models with cross sectional data using two-step generalized estimating equations (GEE) in the quasi-maximum likelihood estimation (QMLE) framework. In the interest of improving efficiency, we propose a grouping estimator to account for the potential spatial correlation in the underlying innovations. We use a Poisson model and a Negative Binomial II model for count data and a Probit model for binary response data to demonstrate the GEE procedure. Under mild weak dependency assumptions, results on estimation consistency and asymptotic normality are provided. Monte Carlo simulations show efficiency gain of our approach in comparison of different estimation methods for count data and binary response data. Finally we apply the GEE approach to study the determinants of the inflow foreign direct investment (FDI) to China.

We propose a bivariate component GARCH-MIDAS model to estimate the long- and short-run components of the variances and covariances. The advantage of our model to the existing DCC-based models is that it uses the same form for both the variances and covariances and that it estimates these moments simultaneously. We apply this model to obtain long- and short-run factor betas for industry test portfolios, where the risk factors are the market, SMB, and HML portfolios. We use these betas in cross-sectional analysis of the risk premia. Among other things, we find that the risk premium related to the short- run market beta is significantly positive, irrespective of the choice of test portfolio. Further, the risk premia for the short-run betas of all the risk factors are significant outside recessions.

Estimating spot covariance is an important issue to study, especially with the increasing availability of high-frequency nancial data. We study the estimation of spot covariance using a kernel method for high-frequency data. In particular, we consider rst the kernel weighted version of realized covariance estimator for the price process governed by a continuous multivariate semimartingale. Next, we extend it to the threshold kernel estimator of the spot covariances when the underlying price process is a discontinuous multivariate semimartingale with nite activity jumps. We derive the asymptotic distribution of the estimators for both xed and shrinking bandwidth. The estimator in a setting with jumps has the same rate of convergence as the estimator for di usion processes without jumps. A simulation study examines the nite sample properties of the estimators. In addition, we study an application of the estimator in the context of covariance forecasting. We discover that the forecasting model with our estimator outperforms a benchmark model in the literature.

Modelling dynamic conditional heteroscedasticity is the daily routine in time series econometrics. We propose a weighted conditional moment estimation to potentially improve the eciency of the QMLE (quasi maximum likelihood estimation). The weights of conditional moments are selected based on the analytical form of optimal instruments, and we nominally decide the optimal instrument based on the third and fourth moments of the underlying error term. This approach is motivated by the idea of general estimation equations (GEE). We also provide an analysis of the eciency of QMLE for the location and variance parameters. Simulations and applications are conducted to show the better performance of our estimators.

We develop a uniform test for detecting and dating explosive behavior of a strictly stationary GARCH(r, s) (generalized autoregressive conditional heteroskedasticity) process. Namely, we test the null hypothesis of a globally stable GARCH process with constant parameters against an alternative where there is an ’abnormal’ period with changed parameter values. During this period, the change may lead to an explosive behavior of the volatility process. It is assumed that both the magnitude and the timing of the breaks are unknown. We develop a double supreme test for the existence of a break, and then provide an algorithm to identify the period of change. Our theoretical results hold under mild moment assumptions on the innovations of the GARCH process. Technically, the existing properties for the QMLE in the GARCH model need to be reinvestigated to hold uniformly over all possible periods of change. The key results involve a uniform weak Bahadur representation for the estimated parameters, which leads to weak convergence of the test statistic to the supreme of a Gaussian Process. In simulations we show that the test has good size and power for reasonably large time series lengths. We apply the test to Apple asset returns and Bitcoin returns.

This paper proposes a dynamic spatial autoregressive quantile model. Using predetermined network information, we study dynamic tail event driven risk using a system of conditional quantile equations. Extending Zhu, Wang, Wang and Härdle (2019), we allow the contemporaneous dependency of nodal responses by incorporating a spatial lag in our model. For example, this is to allow a firm’s tail behavior to be connected with a weighted aggregation of the simultaneous returns of the other firms. In addition, we control for the common factor effects. The instrumental variable quantile regressive method is used for our model estimation, and the associated asymptotic theory for estimation is also provided. Simulation results show that our model performs well at various quantile levels with different network structures, especially when the node size increases. Finally, we illustrate our method with an empirical study. We uncover significant network effects in the spatial lag among financial institutions.

Inflation expectation (IE) is often considered to be an important determinant of actual inflation in modern economic theory, we are interested in investigating the main risk factors that determine its dynamics. We fiirst apply a joint arbitrage-free term structure model across different European countries to obtain estimate for country-specific IE. Then we use the two-component and three-component models to capture the main risk factors. We discover that the extracted common trend for IE is an important driver for each country of interest. Moreover a spatial-temporal copula model is tted to account for the non-Gaussian dependency across countries. This paper aims to extract informative estimates for IE and provide good implications for monetary policies.

The predictability of a high-dimensional time series model in forecasting with large information sets depends not only on the stability of parameters but also depends heavily on the active covariates in the model. Since the true empirical environment can change as time goes by, the variables that function well at the present may become useless in the future. Combined with the instable parameters, finding the most active covariates in the parameter time-varying situations becomes difficult. In this paper, we aim to propose a new method, the Penalized Adaptive Method (PAM), which can adaptively detect the parameter homogeneous intervals and simultaneously select the active variables in sparse models. The newly developed method is able to identify the parameters stability at one hand and meanwhile, at the other hand, can manage of selecting the active forecasting covariates at every different time point. Comparing with the classical models, the method can be applied to high-dimensional cases with different sources of parameter changes while it steadily reduces the forecast error in high- dimensional data. In the out-of-sample bond risk premia forecasting, the Penalized Adaptive Method can reduce the forecasting error(RMSPE and MAPE) around 24% to 50% comparing with the other forecasting methods.

We consider a new procedure for detecting structural breaks in mean for high- dimensional time series. We target breaks happening at unknown time points and locations. In particular, at a fixed time point our method is concerned with either the biggest break in one location or aggregating simultaneous breaks over multiple locations. We allow for both big or small sized breaks, so that we can 1), stamp the dates and the locations of the breaks, 2), estimate the break sizes and 3), make inference on the break sizes as well as the break dates. Our theoretical setup incorporates both temporal and crosssectional dependence, and is suitable for heavy-tailed innovations. We derive the asymptotic distribution for the sizes of the breaks by extending the existing powerful theory on local linear kernel estimation and high dimensional Gaussian approximation to allow for trend stationary time series with jumps. A robust long-run covariance matrix estimation is proposed, which can be of independent interest. An application on detecting structural changes of the US unemployment rate is considered to illustrate the usefulness of our method.

We propose an approach to calibrate the conditional value-at-risk (CoVaR) of financial institutions based on neural network quantile regression. Building on the estimation results we model systemic risk spillover effects across banks by considering the marginal effects of the quantile regression procedure. We adopt a dropout regularization procedure to remedy the well-known issue of overfitting for neural networks, and we provide empirical evidence for the favorable out-of- sample performance of a regularized neural network. We then propose three measures for systemic risk from our fitted results. We find that systemic risk increases sharply during the height of the financial crisis in 2008 and again after a short period of easing in 2011 and 2015. Our approach also allows identifying systemically relevant firms during the financial crisis.

We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the Z-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors.

The CRIX (CRyptocurrency IndeX) has been constructed based on a number of cryptos and provides a high coverage of market liquidity, hu.berlin/crix. The crypto currency market is a new asset market and attracts a lot of investors recently. Surprisingly a market for contingent claims hat not been built up yet. A reason is certainly the lack of pricing tools that are based on solid financial econometric tools. Here a first step towards pricing of derivatives of this new asset class is presented. After a careful econometric pre-analysis we motivate an affine jump diffusion model, i.e., the SVCJ (Stochastic Volatility with Correlated Jumps) model. We calibrate SVCJ by MCMC and obtain interpretable jump processes and then via simulation price options. The jumps present in the cryptocurrency fluctutations are an essential component. Concrete examples are given to establish an OCRIX exchange platform trading options on CRIX.

For change-point analysis of high dimensional time series, we consider a semiparametric model with dynamic structural break factors. The observations are described by a few low dimensional factors with time-invariate loading functions of covariates. The unknown structural break in time models the regime switching e ects introduced by exogenous shocks. In particular, the factors are assumed to be nonstationary and follow a Vector Autoregression (VAR) process with a structural break. In addition, to account for the known spatial discrepancies, we introduce discrete loading functions. We study the theoretical properties of the estimates of the loading functions and the factors. Moreover, we provide both the consistency and the asymptotic convergence results for making inference on the common breakpoint in time. The estimation precision is evaluated via a simulation study. Finally we present two empirical illustrations on modeling the dynamics of the minimum wage policy in China and analyzing a limit order book dataset.

It is a challenging task to understand the complex dependency structures in an ultra-high dimensional network, especially when one concentrates on the tail dependency. To tackle this problem, we consider a network quantile autoregres- sion model (NQAR) to characterize the dynamic quantile behavior in a complex system. In particular, we relate responses to its connected nodes and node specific characteristics in a quantile autoregression process. A minimum contrast estimation approach for the NQAR model is introduced, and the asymptotic properties are studied. Finally, we demonstrate the usage of our model by in- vestigating the financial contagions in the Chinese stock market accounting for shared ownership of companies.

In the present paper we study the dynamics of penalization parameter ? of the least absolute shrinkage and selection operator (Lasso) method proposed by Tibshirani (1996) and extended into quantile regression context by Li and Zhu (2008). The dynamic behaviour of the parameter ? can be observed when the model is assumed to vary over time and therefore the fitting is performed with the use of moving windows. The proposal of investigating time series of ? and its dependency on model characteristics was brought into focus by H¨ardle et al. (2016), which was a foundation of FinancialRiskMeter (http://frm.wiwi.hu-berlin.de). Following the ideas behind the two aforementioned projects, we use the derivation of the formula for the penalization parameter ? as a result of the optimization problem. This reveals three possible effects driving ?; variance of the error term, correlation structure of the covariates and number of nonzero coefficients of the model. Our aim is to disentangle these three effect and investigate their relationship with the tuning parameter ?, which is conducted by a simulation study. After dealing with the theoretical impact of the three model characteristics on ?, empirical application is performed and the idea of implementing the parameter ? into a systemic risk measure is presented. The codes used to obtain the results included in this work are available on http://quantlet.de/d3/ia/.

Inflation expectation is an important indicator for policy makers and financial investors. To capture a more accurate real-time estimate of inflation expectation on the basis of financial markets, we propose an arbitrage-free term structure model across different countries. We first estimate inflation expectation by modeling the nominal and the inflation-indexed bond yields jointly for each country. The joint dynamic model for inflation expectation is a cross sectional state space model combined with a GeoCopula model, which accounts for the default risk and the non Gaussian dependency structure over countries. We discover that the extracted common trend for inflation expectation is an important driver for each country of interest. Moreover, the model extracts informative estimates of inflation expectations and will provide good implications for monetary policies.

Estimating natural rate of unemployment (NAIRU) is important for understanding the joint dynamics of unemployment, inflation, and inflation expectation. However, existing literature falls short in endogenizing inflation expectation together with NAIRU in a model consistent way. We develop and estimate a structural model with forward and backward looking Phillips curve. Inflation expectation is treated as a function of state variables and we use survey data as its observations. We find out that the estimated NAIRU using our methodology tracks the unemployment process closely except for the high inflation period around 1970. Moreover, the estimated Bayesian credible sets are narrower and our model leads to better inflation and unemployment forecasts. These results suggest that monetary policy was very effective during the sample periods and there was not much room for policy improvement.

Inflation expectation is acknowledged to be an important indicator for policy makers and financial investors. To capture a more accurate real-time estimate of inflation expectation on the basis of financial markets, we propose an arbitrage-free model across different countries in a multi-maturity term structure, where we first estimate inflation expectation by modelling the nominal and inflation-indexed bond yields jointly for each country. The Nelson-Siegel model is popular in fitting the term structure of government bond yields, the arbitrage-free model we proposed is the extension of the arbitrage-free dynamic Nelson-Siegel model proposed by Christensen, Diebold and Rudebusch (2011). We discover that the extracted common trend for inflation expectation is an important driver for each country of interest. Moreover, the model will lead to an improved forecast in a benchmark level of inflation and will provide good implications for financial markets.

Estimating natural rate of unemployment (NAIRU) is important for understanding the joint dynamics of unemployment, inflation, and inflation expectation. However, existing literature falls short in endogenizing inflation expectation together with NAIRU in a model consistent way. We develop and estimate a structural model with forward and backward looking Phillips curve. Inflation expectation is treated as a function of state variables and we use survey data as its observations. We find out that the estimated NAIRU using our methodology tracks the unemployment process closely except for the high inflation period around 1970. Moreover, the estimated Bayesian credible sets are narrower and our model leads to better inflation and unemployment forecasts. These results suggest that monetary policy was very effective during the sample periods and there was not much room for policy improvement.

We propose a semiparametric measure to estimate systemic interconnectedness across financial institutions based on tail-driven spill-over effects in a ultra-high dimensional framework. Methodologically, we employ a variable selection technique in a time series setting in the context of a single-index model for a generalized quantile regression framework. We can thus include more financial institutions into the analysis, to measure their interdependencies in tails and, at the same time, to take into account non-linear relationships between them. A empirical application on a set of 200 publicly traded U. S. financial institutions provides useful rankings of systemic exposure and systemic contribution at various stages of financial crisis. Network analysis, its behaviour and dynamics, allows us to characterize a role of each sector in the financial crisis and yields a new perspective of the financial markets at the U. S. financial market 2007 - 2012.

We consider the problem of estimating the conditional quantile of a time series fYtg at time t given covariates Xt, where Xt can ei- ther exogenous variables or lagged variables of Yt . The conditional quantile is estimated by inverting a kernel estimate of the conditional distribution function, and we prove its asymptotic normality and uni- form strong consistency. The performance of the estimate for light and heavy-tailed distributions of the innovations are evaluated by a simulation study. Finally, the technique is applied to estimate VaR of stocks in DAX, and its performance is compared with the existing standard methods using backtesting.

We propose a semiparametric measure to estimate systemic interconnectedness across financial institutions based on tail-driven spill-over effects in a ultra-high dimensional framework. Methodologically, we employ a variable selection technique in a time series setting in the context of a single-index model for a generalized quantile regression framework. We can thus include more financial institutions into the analysis, to measure their interdependencies in tails and, at the same time, to take into account non-linear relationships between them. A empirical application on a set of 200 publicly traded U. S. nancial institutions provides useful rankings of systemic exposure and systemic contribution at various stages of financial crisis. Network analysis, its behaviour and dynamics, allows us to characterize a role of each sector in the financial crisis and yields a new perspective of the nancial markets at the U. S. financial market 2007 - 2012.

We consider the problem of estimating the conditional quantile of a time series fYtg at time t given covariates Xt, where Xt can ei- ther exogenous variables or lagged variables of Yt . The conditional quantile is estimated by inverting a kernel estimate of the conditional distribution function, and we prove its asymptotic normality and uni- form strong consistency. The performance of the estimate for light and heavy-tailed distributions of the innovations are evaluated by a simulation study. Finally, the technique is applied to estimate VaR of stocks in DAX, and its performance is compared with the existing standard methods using backtesting.

We consider theoretical bootstrap "coupling" techniques for nonparametric robust smoothers and quantile regression, and verify the bootstrap improvement. To cope with curse of dimensionality, a variant of "coupling" bootstrap techniques are developed for additive models with both symmetric error distributions and further extension to the quantile regression framework. Our bootstrap method can be used in many situations like constructing confidence intervals and bands. We demonstrate the bootstrap improvement over the asymptotic band theoretically, and also in simulations and in applications to firm expenditures and the interaction of economic sectors and the stock market.

Quantile regression is in the focus of many estimation techniques and is an important tool in data analysis. When it comes to nonparametric specifications of the conditional quantile (or more generally tail) curve one faces, as in mean regression, a dimensionality problem. We propose a projection based single index model specifi- cation. For very high dimensional regressors X one faces yet another dimensionality problem and needs to balance precision vs. dimension. Such a balance may be achieved by combining semiparametric ideas with variable selection techniques.

Quantile regression is in the focus of many estimation techniques and is an important tool in data analysis. When it comes to nonparametric specifications of the conditional quantile (or more generally tail) curve one faces, as in mean regression, a dimensionality problem. We propose a projection based single index model specification. For very high dimensional regressors X one faces yet another dimensionality problem and needs to balance precision vs. dimension. Such a balance may be achieved by combining semiparametric ideas with variable selection techniques.

Financial risk control has always been challenging and becomes now an even harder problem as joint extreme events occur more frequently. For decision makers and government regulators, it is therefore important to obtain accurate information on the interdependency of risk factors. Given a stressful situation for one market participant, one likes to measure how this stress affects other factors. The CoVaR (Conditional VaR) framework has been developed for this purpose. The basic technical elements of CoVaR estimation are two levels of quantile regression: one on market risk factors; another on individual risk factor. Tests on the functional form of the two-level quantile regression reject the linearity. A flexible semiparametric modeling framework for CoVaR is proposed. A partial linear model (PLM) is analyzed. In applying the technology to stock data covering the crisis period, the PLM outperforms in the crisis time, with the justification of the backtesting procedures. Moreover, using the data on global stock markets indices, the analysis on marginal contribution of risk (MCR) defined as the local first order derivative of the quantile curve sheds some light on the source of the global market risk.

Understanding the dynamics of high dimensional non-normal dependency structure is a challenging task. This research aims at attacking this problem by building up a hidden Markov model (HMM) for Hierarchical Archimedean Copulae (HAC), where the HAC represent a wide class of models for high dimensional dependency, and HMM is a statistical technique to describe time varying dynamics. HMM applied to HAC provide flexible modeling for high dimensional non Gaussian time series. Consistency results for both parameters and HAC structures are established in an HMM framework. The model is calibrated to exchange rate data with a VaR application, where the model’s performance is compared with other dynamic models, and in the second application we simulate rainfall process.

Financial risk control has always been challenging and becomes now an even harder problem as joint extreme events occur more frequently. For decision makers and government regulators, it is therefore important to obtain accurate information on the interdependency of risk factors. Given a stressful situation for one market participant, one likes to measure how this stress affects other factors. The CoVaR (Conditional VaR) framework has been developed for this purpose. The basic technical elements of CoVaR estimation are two levels of quantile regression: one on market risk factors; another on individual risk factor. Tests on the functional form of the two-level quantile regression reject the linearity. A flexible semiparametric modeling framework for CoVaR is proposed. A partial linear model (PLM) is analyzed. In applying the technology to stock data covering the crisis period, the PLM outperforms in the crisis time, with the justification of the backtesting procedures. Moreover, using the data on global stock markets indices, the analysis on marginal contribution of risk (MCR) defined as the local first order derivative of the quantile curve sheds some light on the source of the global market risk.

Understanding the dynamics of high dimensional non-normal dependency structure is a challenging task. This research aims at attacking this problem by building up a hidden Markov model (HMM) for Hierarchical Archimedean Copulae (HAC), where the HAC represent a wide class of models for high dimensional dependency, and HMM is a statistical technique to describe time varying dynamics. HMM applied to HAC provide flexible modeling for high dimensional non Gaussian time series. Consistency results for both parameters and HAC structures are established in an HMM framework. The model is calibrated to exchange rate data with a VaR application, where the model's performance is compared with other dynamic models, and in the second application we simulate rainfall process.

It is an undisputed fact that weather risk increases over time due to climate change. However, qualification of this statement with regard to the type of weather risk and geographical location is needed. We investigate the application of novel statistical tools for assessing changes in weather risk over time. We apply local t-test, change point tests and Mann-Kendall test as well as quantile regression to weather risk indicators that are relevant from the viewpoint of agricultural production. Our results show that weather risk follows different pattern depending on the type of risk and the location.

Conditional quantile curves provide a comprehensive picture of a response contingent on explanatory variables. Quantile regression is a technique to estimate such curves. In a flexible modeling framework, a specific form of the quantile is not a priori fixed. Indeed, the majority of applications do not per se require specific functional forms. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimate of the conditional quantile curve requires to consider a balance between local curvature and variance. In this paper, we analyze a method based on a local model selection technique that provides an adaptive estimate. Theoretical properties on mimicking the oracle choice are offered and applications to stock market and weather analysis are presented.

Statistische Prognosen basieren auf der Annahme, dass ein funktionaler Zusammenhang zwischen der zu prognostizierenden Variable y und anderen j-dimensional beobachtbaren Variablen x = (x1,...xl) besteht. Kann der funktionale Zusammenhang geschätzt werden, so kann im Prinzip für jedes x der zugehörige Wert y prognostiziert werden. Bei den meisten Anwendungen wird angenommen, dass der funktionale Zusammenhang einem niedrigdimensionalen parametrischen Modell entspricht oder durch dieses zumindest gut wiedergegeben wird. Ein Beispiel im univariaten Fall ist das lineare Modell y = b0 + b1x. Sind die beiden unbekannten Parameter b0 und b1 mithilfe historischer Daten geschätzt, so lässt sich für jedes gegebene x sofort der zugehörige Wert y prognostizieren. Allerdings besteht hierbei die Gefahr, dass der wirkliche funktionale Zusammenhang nicht dem gewählten Modell entspricht. Dies kann infolge zu schlechten Prognosen führen. Nichtparametrische Verfahren gehen ebenfalls von einem funktionalen Zusammenhang aus, geben aber kein festes parametrisches Modell vor und zwängen die Daten damit in kein Prokrustes Bett. Sie sind deshalb hervorragend geeignet, um 1) Daten explorativ darzustellen, 2) parametrische Modelle zu überprüfen und 3) selbst als Schätzer für den funktionalen Zusammenhang zu dienen (Cleveland [2], Cleveland und Devlin [3]). Nichtparametrische Verfahren können daher problemlos auch zur Prognose eingesetzt werden. Dieses Kapitel ist wie folgt strukturiert. Abschnitt 9.2 stellt nichtparametrische Verfahren vor und erläutert deren grundsätzliche Struktur. Der Schwerpunkt liegt auf dem univariaten Regressionsmodell und auf der Motivation der vorgestellten Verfahren. Abschnitt 9.3 präsentiert eine praktische Anwendung für eine Zeitreihe von Wechselkursvolatilitäten. Es werden Prognosen mit nichtparametrischen Verfahren berechnet und deren Güte mit den Prognosen eines AR(1)-Zeitreihenmodells verglichen, vgl. auch Kapitel 14 dieses Buches. Es zeigt sich für die gewählte Anwendung, dass das parametrische Modell die Daten sehr gut erfasst. Das nichtparametrische Modell liefert in dieser Anwendung keine bessere Prognosegüte. Zugleich veranschaulicht die Anwendung, wie nichtparametrische Verfahren für die Modelvalidierung eingesetzt werden können. Und natürlich zeigt es auch, wie solche Verfahren für Prognosen eingesetzt werden können. Abschnitt 9.4 präsentiert die Literatur, die für weitere Lektüre herangezogen werden kann. Alle praktischen Beispiele im Text, welche mit dem Symbol versehen sind, lassen sich von der Addresse www.quantlet.de herunterladen.

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by nonparametric regression. The subjective density is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by nonparametric regression. The subjective density is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by nonparametric regression. The subjective density is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.

Conditional quantile curves provide a comprehensive picture of a response contingent on explanatory variables. Quantile regression is a technique to estimate such curves. In a flexible modeling framework, a specific form of the quantile is not a priori fixed. Indeed, the majority of applications do not per se require specific functional forms. This motivates a local parametric rather than a global fixed model fitting approach. A nonparametric smoothing estimate of the conditional quantile curve requires to consider a balance between local curvature and variance. In this paper, we analyze a method based on a local model selection technique that provides an adaptive estimate. Theoretical properties on mimicking the oracle choice are offered and applications to stock market and weather analysis are presented.

Heutzutage sind viele verschiedene Machine Learning Algorithmen vorhanden. Als Konsequenz, mehr als ein Algorithmus kann auf ein ausgewähltes Problem angewandt werden. Dies führt zu einer Frage, wie unterschiedlich in solch einem Fall die Ergebnisse von den Algorithmen sein werden. In einem Versuch, diese Frage zu beantworten, werden in der folgenden Arbeit die Ergebnisse von vier sehr bekannten Supervised Learning Algorithmen, die auf ein binäres Klassifikationsproblem angewendet wurden, verglichen., Today there are a lot of various machine learning algorithms available. As a consequence, when it comes to a specific problem, more than one algorithm can be applied to solve it. Therefore, a question is posed, about how different the results would be in such a case. In an attempt answer this question, this thesis compares the results of four well-known supervised learning algorithms, applied to a binary classification problem.

Wir entwickeln einen neuen Ansatz zur Schätzung vom Conditional Value-at-Risk (CoVaR) von Finanzinstituten. Unsere Methode basiert auf Neural Network Quantilregression. Aufbauend auf den Ergebnissen der Schätzung modellieren wir Risiko-Spillover-Effekte zwischen Banken, indem wir marginale Effekte der Quantilregression berechnen. Wir erhalten ein zeitlich veränderliches Risikonetzwerk, dargestellt durch eine Adjazenzmatrix. Daraufhin schlagen wir drei systemische Risikomaße vor. Der Systemic Fragility Index und der Systemic Hazard Index identifizieren die anfälligsten und die gefährlichsten Firmen im Finanzsystem. Als drittes Maß schlagen wir den Systemic Network Risk Index vor, welcher das allgemeine systemische Risiko im Finanzsystem misst. Wir wenden unsere Methode auf die global systemrelevanten Banken aus den Vereinigten Staaten an. Unsere Resultate bestätigen bestehende Studien. Wir fanden heraus, dass das systemische Risiko während des Höhepunkts der Finanzkrise 2008 stark anstieg und nochmal in 2011 und 2015 nach einer kurzen Phase der Beruhigung., We propose a novel approach to estimate the conditional value at risk (CoVaR) of financial institutions. Our approach is based on neural network quantile regression. Building on the estimation results we model systemic risk spillover effects across banks by considering the marginal effects of the quantile regression procedure. We obtain a time-varying risk network represented by an adjacency matrix. We then propose three measures for systemic risk. The Systemic Fragility Index and the Systemic Hazard Index are measures to identify the most vulnerable and most critical firms in the financial system, respectively. As a third risk measure we propose the Systemic Network Risk Index which represents the overall level of systemic risk. We apply our methodology to the global systemically relevant banks from the United States in a time period from 2007 until 2018. Our results are similar to previous studies about systemic risk. We find that systemic risk increased sharply during the height of the financial crisis in 2008 and again after a short period of easing in 2011 and 2015.

Zentrale Grenzwertsätze zählen zu den bedeutendsten Resultaten der modernen Wahrscheinlichkeitstheorie. Sie sind unverzichtbar für grundlegende Methoden der angewandten Mathematik – so auch maßgeblich für die mathematische Statistik. In der vorliegenden Arbeit werden in einem ersten Schritt – mit den Sätzen von Moivre- Laplace, Feller-Lévy und Lindeberg-Feller – die fundamentalen theoretischen Konzepte ausführlich erläutert und bewiesen. Darüberhinaus findet sich, insbesondere für den Zentralen Grenzwertsatz von Feller-Lévy, eine kurze Diskussion der Konvergenzgüte. Im zweiten Teil werden mögliche Anwendungsbereiche der Zentralen Grenzwertsätze in der Inferenzstatistik aufgezeigt und mit praktischen Beispielen unterlegt. Hierbei stehen die statistische Intervallschätzung und statistische Hypothesentests für den Erwartungswert im Mittelpunkt. Diese Arbeit versteht sich als eine Art erster Überblick bzw. als Einstieg in die Thematik für Studenten der Mathematik und Statistik mit maßtheoretischen Vorkenntnissen. Central limit theorems are among the most important results of modern probability theory. They are indispensable for basic methods in applied mathematics – such as mathematical statistics. In a first step, the fundamental theoretical concepts, as there are the theorems of Moivre-Laplace, Feller-Lévy and Lindeberg-Feller, are comprehensively presented and proven. Furthemore there is a brief discussion of the quality of convergence, especially for the central limit theorem of Feller-Lévy. In the second part possible areas of application in inferential statistics are pointed out and underlined by practical examples. This work focuses thereby on statistical interval estimation and statistical hypothesis testing for the expected value. This work must be seen as a first overview and introduction to the subject for students of mathematics and statistics with basic knowledge in measure-theory.

This paper applies the spatiotemporal technology to modeling inflation rates of eight euro zone countries in a time interval from 1998 to 2008. While applying Gaussian copula to increase the flexibility of the multivariate model, I use the weighted pairwise composite likelihood method suggested by Lindsay (1988), Cox and Reid (2004) to tackle the computational problem. Due to the existence of exogenous shock, the fitted series show noises and vibrate around the real series. These noises can be eliminated by a three-term moving average smoother, indicating that the model can explain the majority of the spatiotemporal dependence of inflation rates in these countries.

This essay presents a marketing problematic along with a way of solving it with the help of statistical tools. Precisely, a Recommender System is built to address a marketing problem for a supermarket in Germany. Both the the- oretical and the practical aspects of the use of Machine Learning methods are underlined. Our focus is oriented in two parts. First, we define precisely a problem, from the conceptual meaning to its natural mathematical transla- tion. Second, we provide an analysis that is anchored to business constraints, on top of being an academic paper. Highlight is made on unifying notations for this specific problem, and on comparing different methods before and after their implementation. This work is designed to fulfill the Master’s thesis re- quirements with advanced statistical approach. Mathematical background is emphasized in parallel with hands-on implementation using the open source software R.

Die Master-Thesis analysiert den Britische Gilts Markt mit AFDNS Modell. Vier unbekannte Faktoren sind in unserem Modell eingeschlossen. Mit "Kalman Filter" sind das gemeinsame Modellieren der nominalen und Inflation-bereinigten Renditen optimiziert. This thesis completes a joint estimation of U.K. Gilts market using an Arbitrage-Free dynamic Nelson-Siegel (AFDNS) model with four latent factors. The joint modelling of nominal and inflation-indexed yield curves are optimized through the use of Kalman filtering technique. The estimates of inflation expectations are obtained by subtracting inflation risk premiums from the differences between yields on comparable-maturity nominal and real bonds, the so called break-even inflation (BEI) rates.

In den Finanzmarkt gibt es viele verschiedene Risikofaktoren rund um ein festgelegtes Finanzunternehmen. Zum Beispiel, Kreditrisiko, Liquiditätsrisiko und das Marktrisiko. Andere Unternehmen können sich auch auf diese unternehmen beeinflussen. Um die relevanten Risikofaktoren zu identifizieren und die mögliche Ansteckungseffekt zu erkennen. Die Auswirkungen von anderen Unternehmen zu dieser bestimmten unternehmen sind wichtig. Der Conditonal Value at Risk (CoVaR) können diese Risiken zu messen und wird in diesem Papier aufgebracht werden. Um CoVaR abzuschätzen, Quantilsregresssion ist eine grundlegende Methode. Denn die Auswirkung von anderen Risikofaktoren auf diese angegebene Unternehmen ist oft nicht linear, das Single Index Model (SIM) als semiparametrischer Schätzung spielt eine wichtige Rolle. Auswahl der relevanten Risikofaktoren kann durch Variable Auswahltechnik gelöst werden. Kurz gesagt, Quantilsregression für Single Index Model mit Variablen Auswahltechnik würde in Bezug auf die Finanzdaten in dieser Papier durchgeführt werden, würde die Bewertung durch Backtesting durchgeführt werden. In financial market there are many different risk factors surrounding a specified financial firm. For example, credit risk, liquidity risk and market risk. Other firms can affect this firm as well. To identify the relevant risk factors and to detect the possible contagion effects from other firms to this specified firm are important. Conditional value at risk (CoVaR) can measure these risks and will be applied in this paper. To estimate CoVaR quantile regresssion is a basic method. Since the impact from other risk factors to this specified financial firm is often nonlinear, single index model (SIM) as a semiparametric estimation plays an important role. Selecting the relevant risk factors can be solved by variable selection technique. Briefly, quantile regression for single index model associated with variable selection technique would be carried out in terms of financial data in this paper, the evaluation would be conducted by Backtesting.

In dieser Masterarbeit zeigen wir, wie nichtparametrische Regressionsverfahren verwendet werden können, um Monitoring-Systeme für Industrieanlagen zu entwickeln. Da die verwendeten Datensätze oft sehr groß sind und Monitoring in Echtzeit durchgeführt wird, stellen wir zwei verschiedene Ansätze zur Reduzierung der Rechenzeit der nichtparametrischen Methoden vor. Beide Ansätze werden im Hinblick auf Laufzeit und Approximationsfehler verglichen und ihre Eigenschaften anhand einer Simulationsstudie veranschaulicht. Wir wenden unsere Methode auf reale Daten einer industriellen Versorgungstechnik-Anlage an. In this thesis we show how to use nonparametric regression techniques to develop monitoring systems for industrial machinery. Since data sets are often very big and monitoring has to be done online we present two ifferent approaches to speed up computational time of the nonparametric methods. Both approaches are compared regarding run-time and approximation error and their properties are illustrated in a simulation study. We apply our methodology to real data from an industrial supply engineering machine.