Melanie Schienle

Nonparametric Regression with Nonparametrically Generated Covariates

We analyze the properties of non- and semiparametric estimation procedures involving nonparametric regression with generated covariates. Such estimators appear in numerous econometric applications, including nonparametric estimation of simultaneous equation models, sample selection models, treatment effect models, and censored regression models, but so far there seems to be no unified theory to establish their statistical properties. Our paper provides such results, allowing to establish asymptotic properties like rates of consistency or asymptotic normality for a wide range of semi- and nonparametric estimators. We also show how to account for the presence of nonparametrically generated regressors when computing standard errors.

Semiparametric Estimation with Generated Covariates

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 infinite-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.

Nonparametric kernel density estimation near the boundary

Standard fixed symmetric kernel-type density estimators are known to encounter problems for positive random variables with a large probability mass close to zero. It is shown that, in such settings, alternatives of asymmetric gamma kernel estimators are superior, but also differ in asymptotic and finite sample performance conditionally on the shape of the density near zero and the exact form of the chosen kernel. Therefore, a refined version of the gamma kernel with an additional tuning parameter adjusted according to the shape of the density close to the boundary is suggested. A data-driven method for the appropriate choice of the modified gamma kernel estimator is also provided. An extensive simulation study compares the performance of this refined estimator to those of standard gamma kernel estimates and standard boundary corrected and adjusted fixed kernels. It is found 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.

Capturing the Zero: A New Class of Zero-Augmented Distributions and Multiplicative Error Processes

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 at high frequencies, such as cumulated trading volumes. 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 both liquid and illiquid NYSE stocks, we show that the model captures the dynamic and distributional properties of the data well and is able to correctly predict future distributions.

Nonparametric estimation of risk-neutral densities

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.

Systemic Risk Spillovers in the European Banking and Sovereign Network

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.

Generated Covariates in Nonparametric Estimation: A Short Review

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.

Nonparametric Nonstationary Regression with Many Covariates

This article studies nonparametric estimation of a regression model for d ≥ 2 potentially nonstationary 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 modeling flexibility. Estimation of an additive conditional mean function can be conducted under weak conditions: It is sufficient that the response Y and all univariate X and pairs of bivariate marginal components X of the vector of all covariates X are (potentially nonstationary) β-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. Under different types of independence assumptions, asymptotic distributions are derived for the general case of a (potentially nonstationary) β–null Harris recurrent noise term e but also for the special case of e 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. JEL Classification: C14, C22

Beyond Dimension two: A Test for Higher-Order Tail Risk

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 2. 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 2007/2008 on, however, higher order dependencies generally increase and require a multivariate tail model in all cases.

Testing for an Omitted Multiplicative Long-Term Component in GARCH Models

We consider the problem of testing for an omitted multiplicative long-term component in GARCH-type models. Under the alternative, there is a two-component model with a short-term GARCH component th...