Essays on Modern Econometrics and Machine Learning

Diese Dissertation behandelt verschiedene Aspekte moderner Ökonometrie und Machine Learnings. Kapitel 2 stellt einen neuen Schätzer für die Regressionsparameter in einem Paneldatenmodell mit interaktiven festen Effekten vor. Eine Besonderheit unserer Methode ist die Modellierung der factor loadings durch nichtparametrische Funktionen. Wir zeigen die root-NT-Konvergenz sowie die asymptotische Normalverteilung unseres Schätzers. Kapitel 3 betrachtet die rekursive Schätzung von Quantilen mit Hilfe des stochastic gradient descent (SGD) Algorithmus mit Polyak-Ruppert Mittelwertbildung. Der Algorithmus ist rechnerisch und Speicher-effizient verglichen mit herkömmlichen Schätzmethoden. Unser Fokus ist die Untersuchung des nichtasymptotischen Verhaltens, indem wir eine exponentielle Wahrscheinlichkeitsungleichung zeigen. In Kapitel 4 stellen wir eine neue Methode zur Kalibrierung von conditional Value-at-Risk (CoVaR) basierend auf Quantilregression mittels Neural Networks vor. Wir modellieren systemische Spillovereffekte in einem Netzwerk von systemrelevanten Finanzinstituten. Eine Out-of-Sample Analyse zeigt eine klare Verbesserung im Vergleich zu einer linearen Grundspezifikation. Im Vergleich mit bestehenden Risikomaßen eröffnet unsere Methode eine neue Perspektive auf systemisches Risiko. In Kapitel 5 modellieren wir die gemeinsame Dynamik von Kryptowährungen in einem nicht-stationären Kontext. Um eine Analyse in einem dynamischen Rahmen zu ermöglichen, stellen wir eine neue vector error correction model (VECM) Spezifikation vor, die wir COINtensity VECM nennen.This thesis focuses on different aspects of the union of modern econometrics and machine learning. Chapter 2 considers a new estimator of the regression parameters in a panel data model with unobservable interactive fixed effects. A distinctive feature of the proposed approach is to model the factor loadings as a nonparametric function. We show that our estimator is root-NT-consistent and asymptotically normal, as well that it reaches the semiparametric efficiency bound under the assumption of i.i.d. errors. Chapter 3 is concerned with the recursive estimation of quantiles using the stochastic gradient descent (SGD) algorithm with Polyak-Ruppert averaging. The algorithm offers a computationally and memory efficient alternative to the usual empirical estimator. Our focus is on studying the nonasymptotic behavior by providing exponentially decreasing tail probability bounds under minimal assumptions. In Chapter 4 we propose a novel approach to calibrate the conditional value-at-risk (CoVaR) of financial institutions based on neural network quantile regression. We model systemic risk spillover effects in a network context across banks by considering the marginal effects of the quantile regression procedure. An out-of-sample analysis shows great performance compared to a linear baseline specification, signifying the importance that nonlinearity plays for modelling systemic risk. A comparison to existing network-based risk measures reveals that our approach offers a new perspective on systemic risk. In Chapter 5 we aim to model the joint dynamics of cryptocurrencies in a nonstationary setting. In particular, we analyze the role of cointegration relationships within a large system of cryptocurrencies in a vector error correction model (VECM) framework. To enable analysis in a dynamic setting, we propose the COINtensity VECM, a nonlinear VECM specification accounting for a varying system-wide cointegration exposure

On cointegration and cryptocurrency dynamics

This paper aims to model the joint dynamics of cryptocurrencies in a nonstationary setting. In particular, we analyze the role of cointegration relationships within a large system of cryptocurrencies in a vector error correction model (VECM) framework. To enable analysis in a dynamic setting, we propose the COINtensity VECM, a nonlinear VECM specification accounting for a varying systemwide cointegration exposure. Our results show that cryptocurrencies are indeed cointegrated with a cointegration rank of four. We also find that all currencies are affected by these long term equilibrium relations. The nonlinearity in the error adjustment turned out to be stronger during the height of the cryptocurrency bubble. A simple statistical arbitrage trading strategy is proposed showing a great in-sample performance, whereas an out-of-sample analysis gives reason to treat the strategy with caution.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659H2020 Research and Innovation ProgramPeer Reviewe

Modelling systemic risk using neural network quantile regression

We propose a novel 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 in a network context across banks by considering the marginal effects of the quantile regression procedure. An out-of-sample analysis shows great performance compared to a linear baseline specification, signifying the importance that nonlinearity plays for modelling systemic risk. We then propose three network-based measures from our fitted results. First, we use the Systemic Network Risk Index (SNRI) as a measure for total systemic risk. A comparison to the existing network-based risk measures reveals that our approach offers a new perspective on systemic risk due to the focus on the lower tail and to the allowance for nonlinear effects. We also introduce the Systemic Fragility Index (SFI) and the Systemic Hazard Index (SHI) as firm-specific measures, which allow us to identify systemically relevant firms during the financial crisis.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/501100001659Peer Reviewe

Shapley Curves: A Smoothing Perspective

Originating from cooperative game theory, Shapley values have become one of the most widely used measures for variable importance in applied Machine Learning. However, the statistical understanding of Shapley values is still limited. In this paper, we take a nonparametric (or smoothing) perspective by introducing Shapley curves as a local measure of variable importance. We propose two estimation strategies and derive the consistency and asymptotic normality both under independence and dependence among the features. This allows us to construct confidence intervals and conduct inference on the estimated Shapley curves. The asymptotic results are validated in extensive experiments. In an empirical application, we analyze which attributes drive the prices of vehicles

Modelling Systemic Risk using Neural Network Quantile Regression

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

A projection based approach for interactive fixed effects panel data models

This paper presents a new approach to estimation and inference in panel data models with interactive fixed effects, where the unobserved factor loadings are allowed to be correlated with the regressors. A distinctive feature of the proposed approach is to assume a nonparametric specification for the factor loadings, that allows us to partial out the interactive effects using sieve basis functions to estimate the slope parameters directly. The new estimator adopts the well-known partial least squares form, and its $\sqrt{NT}$-consistency and asymptotic normality are shown. Later, the common factors are estimated using principal component analysis (PCA), and the corresponding convergence rates are obtained. A Monte Carlo study indicates good performance in terms of mean squared error. We apply our methodology to analyze the determinants of growth rates in OECD countries