Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

A supreme test for periodic explosive GARCH

Stefan Richter
Weining Wang
Wei Biao Wu

Abstract:
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.

Keywords:
GARCH, IGARCH, Change-point Analysis, Concentration Inequalities, Uniform Test

JEL Classification:
C00

Using generalized estimating equations to estimate nonlinear models with
spatial data

Cuicui Lu
Weining Wang
Jeffrey M. Wooldridge

Abstract:
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.

Keywords:
quasi-maximum likelihood estimation; generalized estimating equations; nonlinear
models; spatial dependence; count data; binary response data; FDI equation

JEL Classification:
C13, C21, C35, C51

Data Analytics Driven Controlling: bridging statistical modeling and managerial
intuition

Kainat Khowaja
Danial Saef
Sergej Sizov
Wolfgang Karl Härdle

Abstract:
Strategic planning in a corporate environment is often based on experience and
intuition, although internal data is usually available and can be a valuable
source of information. Predicting merger & acquisition (M&A) events is at the
heart of strategic management, yet not sufficiently motivated by data
analytics driven controlling. One of the main obstacles in using e.g. count data
time series for M&A seems to be the fact that the intensity of M&A is time
varying at least in certain business sectors, e.g. communications. We propose a
new automatic procedure to bridge this obstacle using novel statistical methods.
The proposed approach allows for a selection of adaptive windows in count data
sets by detecting significant changes in the intensity of events. We test the
efficacy of the proposed method on a simulated count data set and put it into
action on various M&A data sets. It is robust to aberrant behaviour and
generates accurate forecasts for the evaluated business sectors. It also
provides guidance for an a-priori selection of fixed windows for forecasting.
Furthermore, it can be generalized to other business lines, e.g. for managing
supply chains, sales forecasts, or call center arrivals, thus giving managers
new ways for incorporating statistical modeling in strategic planning decisions.

Keywords:
-

JEL Classification:
C00

Tail Risk Network Effects in the Cryptocurrency Market during the COVID-19
Crisis

Rui Ren
Michael Althof
Wolfgang Karl Härdle

Abstract:
Cryptocurrencies are gaining momentum in investor attention, are about to become
a new asset class, and may provide a hedging alternative against the risk of
devaluation of fiat currencies following the COVID-19 crisis. In order to
provide a thorough understanding of this new asset class, risk indicators need
to consider tail risk behaviour and the interdependencies between the
cryptocurrencies not only for risk management but also for portfolio
optimization. The tail risk network analysis framework proposed in the paper is
able to identify individual risk characteristics and capture spillover effect in
a network topology. Finally we construct tail event sensitive portfolios and
consequently test the performance during an unforeseen COVID-19 pandemic.

Keywords:
Cryptocurrencies, Network Dynamics, Portfolio Optimization, Quantile Regression,
Systemic Risk, Financial Risk Meter

JEL Classification:
C00

Surrogate Models for Optimization of Dynamical Systems Kainat Khowaja Mykhaylo Shcherbatyy Wolfgang Karl Härdle Abstract: Surrogate models using a suitable orthogonal decomposition and radial basis functions have been proposed by many researchers to reduce the computational complexity of numerical solutions to optimization problems. However, these reduced-order models result in low accuracy, sometimes due to inappropriate initial sampling or the occurrence of optima at vertices. This paper provides an improved intelligent data-driven mechanism for constructing low-dimensional surrogate models using alternative memory-based sampling strategies in an iterative algorithm. Furthermore, the application of surrogate models to optimal control problems is extended.
It is shown that surrogate models with Latin hypercube sampling dominate variable-order methods in optimization computation time while maintaining accuracy. They are also shown to be robust to nonlinearities in the model. Therefore, these computationally efficient predictive surrogate models are applicable in various fields, especially for solving inverse problems and optimal control problems, some examples of which are shown in this paper. Keywords: Proper Orthogonal Decomposition, SVD, Radial Basis Functions, Optimization, Surrogate Models, Smart Data Analytics, Parameter Estimation JEL Classification: C00

FRM Financial Risk Meter for Emerging Markets

Souhir Ben Amor
Michael Althof
Wolfgang Karl Härdle

Abstract:
The fast-growing Emerging Market (EM) economies and their improved transparency
and liquidity have attracted international investors. However, the external
price shocks can result in a higher level of volatility as well as domestic
policy instability. Therefore, an efficient risk measure and hedging strategies
are needed to help investors protect their investments against this risk. In
this paper, a daily systemic risk measure, called FRM (Financial Risk Meter) is
proposed. The FRM@ EM is applied to capture systemic risk behavior embedded in
the returns of the 25 largest EMs’ FIs, covering the BRIMST (Brazil, Russia,
India, Mexico, South Africa, and Turkey), and thereby reflects the financial
linkages between these economies. Concerning the Macro factors, in addition to
the Adrian & Brunnermeier (2016) Macro, we include the EM sovereign yield spread
over respective US Treasuries and the above-mentioned countries’ currencies. The
results indicated that the FRM of EMs’ FIs reached its maximum during the US
financial crisis following by COVID 19 crisis and the Macro factors explain the
BRIMST’ FIs with various degrees of sensibility. We then study the relationship
between those factors and the tail event network behavior to build our policy
recommendations to help the investors to choose the suitable market for
investment and tail-event optimized portfolios. For that purpose, an overlapping
region between portfolio optimization strategies and FRM network centrality is
developed. We propose a robust and well-diversified tail-event and cluster risk-
sensitive portfolio allocation model and compare it to more classical
approaches.

Keywords:
FRM (Financial Risk Meter), Lasso Quantile Regression, Network Dynamics,
Emerging Markets, Hierarchical Risk Parity

JEL Classification:
C30, C58, G11, G15, G21

K-expectiles clustering

Bingling Wang
Yingxing Li
Wolfgang Karl Härdle

Abstract:
K-means clustering is one of the most widely-used partitioning algorithm in
cluster analysis due to its simplicity and computational efficiency, but it may
not provide ideal clustering results when applying to data with non-spherically
shaped clusters. By considering the asymmetrically weighted distance, We propose
the K-expectile clustering and search the clusters via a greedy algorithm that
minimizes the within cluster τ-variance. We provide algorithms based on two
schemes: the fixed τ clustering, and the adaptive τ clustering. Validated by
simulation results, our method has enhanced performance on data with asymmetric
shaped clusters or clusters with a complicated structure. Applications of our
method show that the fixed τ clustering can bring some flexibility on
segmentation with a decent accuracy, while the adaptive τ clustering may yield
better performance. All calculation can be redone via quantlet.com.

Keywords:
clustering, expectiles, asymmetric quadratic loss, image segmentation

JEL Classification:
C00

Understanding Smart Contracts: Hype or Hope?

Elizaveta Zinovyev
Raphael C. G. Reule
Wolfgang Karl Härdle

Abstract:
Smart Contracts are commonly considered to be an important component or even a
key to many business solutions in an immense variety of sectors and promises to
securely increase their individual efficiency in an ever more digitized
environment. Introduced in the early 1990’s, the technology has gained a lot of
attention with its application to blockchain technology to an extent, that can
be considered a veritable hype. Reflecting the growing institutional interest,
this intertwined exploratory study between statistics, information technology,
and law contrasts these idealistic stories with the data reality and provides a
mandatory step of understanding the matter, before any further relevant
applications are discussed as being “factually” able to replace traditional
constructions. Besides fundamental flaws and application difficulties of
currently employed Smart Contracts, the technological drive and enthusiasm
backing it may however serve as a jump-off board for future developments
thrusting well in the presently unshakeable traditional structures.

Keywords:
Cryptocurrency, Smart Contract, Ethereum, CRIX

JEL Classification:
G02, G11, G12, G14, G15, G23

CATE Meets ML: Conditional Average Treatment Effect and Machine Learning

Daniel Jacob

Abstract:
For treatment effects - one of the core issues in modern econometric analysis -
prediction and estimation are flip-sides of the same coin. As it turns out,
machine learning methods are the tool for generalized prediction models.
Combined with econometric theory allows us to estimate not only the average but
a personalized treatment effect - the conditional average treatment effect
(CATE). In this tutorial, we give an overview of novel methods, explain them in
detail, and apply them via Quantlets in real data applications. We study the
effect that microcredit availability has on the amount of money borrowed and if
the 401(k) pension plan eligibility has an impact on net financial assets, as
two empirical examples. The presented toolbox of methods contains meta-
learners, like the Doubly-Robust, the R-, T- and X-learner, and methods that are
specially designed to estimate the CATE like the causal BART and the generalized
random forest. In both, the microcredit and the 401(k) example, we find a
positive treatment effect for all observations but diverse evidence of treatment
effect heterogeneity. An additional simulation study, where the true treatment
effect is known, allows us to compare the different methods and to observe
patterns and similarities.

Keywords:
Causal Inference, CATE, Machine Learning, Tutorial

JEL Classification:
C00

Coins with benefits: on existence, pricing kernel and risk premium of
cryptocurrencies

Cathy Yi-Hsuan Chen
Dmitri Vinogradov

Abstract:
Cryptocurrencies come with benefits, such as anonymity of payments and positive
network effects of user adoption, and transaction risks including unconfirmed
transactions, hacks, and frauds. They compete with central-bank-regulated money
but consumers may prefer one currency over the other. In our arbitrage-free
world utility from consumption depends on benefits, which are governed by
distinct stochastic processes, implying incomplete markets and distinct pricing
kernels. We characterize the cryptocurrency kernels, evaluate the otherwise
unobservable benefits, and show their contribution to pricing. The model
explains both the co-existence of the two currencies and the high volatility of
the cryptocurrency price.

Keywords:
Bitcoin, cryptocurrency, pricing kernel, currency competition

JEL Classification:
A1, D0, E21, G12

Rodeo or Ascot: which hat to wear at the crypto race?

Konstantin Häusler
Wolfgang Karl Härdle

Abstract:
This paper sheds light on the dynamics of the cryptocurrency (CC) sector. By
modeling its dynamics via a stochastic volatility with correlated jumps (SVCJ)
model in combination with several rolling windows, it is possible to capture the
extreme ups and downs of the CC market and to understand its dynamics. Through
this approach, we obtain time series for each parameter of the model. Even
though parameter estimates change over time and depend on the window size,
several recurring patterns are observable which are robust to changes of the
window size and supported by clustering of parameter estimates: during bullish
periods, volatility stabilizes at low levels and the size and volatility of
jumps in mean decreases. In bearish periods though, volatility increases and
takes longer to return to its long-run trend. Furthermore, jumps in mean and
jumps in volatility are independent. With the rise of the CC market in 2017, a
level shift of the volatility of volatility occurred.

Keywords:
Cryptocurrency, SVCJ, Market Dynamics, Stochastic Volatility

JEL Classification:
C51, C58, G15

Financial Risk Meter based on Expectiles

Rui Ren
Meng-Jou Lu
Yingxing Li
Wolfgang Karl Härdle

Abstract:
The Financial Risk Meter (FRM) is an established mechanism that, based on
conditional Value at Risk (VaR) ideas, yields insight into the dynamics of
network risk. Originally, the FRM has been composed via Lasso based quantile
regression, but we here extend it by incorporating the idea of expectiles, thus
indicating not only the tail probability but rather the actual tail loss given a
stress situation in the network. The expectile variant of the FRM enjoys several
advantages: Firstly, the coherent and multivariate tail risk indicator
conditional expectile-based VaR (CoEVaR) can be derived, which is sensitive to
the magnitude of extreme losses. Next, FRM index is not restricted to an index
compared to the quantile based FRM mechanisms, but can be expanded to a set of
systemic tail risk indicators, which provide investors with numerous tools in
terms of diverse risk preferences. The power of FRM also lies in displaying FRM
distribution across various entities every day. Two distinct patterns can be
discovered under high stress and during stable periods from the empirical
results in the United States stock market. Furthermore, the framework is able to
identify individual risk characteristics and capture spillover effects in a
network.

Keywords:
expectiles, EVaR, CoEVaR, expectile lasso regression, network analysis, systemic
risk, Financial Risk Meter

JEL Classification:
C00

Von den Mühen der Ebenen und der Berge in den Wissenschaften

Annette Vogt

Abstract:
Der Mathematiker und Statistiker E. J. Gumbel führte eine Doppelexistenz – als
Mathematiker und Statistiker von 1923 bis zu seiner Vertreibung 1932 an der
Universität Heidelberg und als politischer Autor. Auch im Exil in Frankreich
behielt er diese Doppeltätigkeit bei, verfasste mathematische Arbeiten und
publizierte Artikel gegen das NS-Regime in Exil-Zeitschriften. Sein Hauptwerk
„Statistics of Extremes“ erschien 1958 in New York (eine Reprint-Ausgabe 2013).
Die „Wiederentdeckung“ des „politischen Gumbel“ begann 2012 und fast zeitgleich
die „Wiederentdeckung“ des „mathematischen Gumbel“. Die Anwendungen der „Gumbel
Distribution“ und der Gumbel-Copula zur Modellierung stochastischer
Abhängigkeiten weckten das Interesse an der Person Gumbel und seinen Leistungen.
Im Artikel werden neue Forschungsergebnisse zu E. J. Gumbel vorgestellt.

Keywords:
Emil J. Gumbel – Mathematiker, Pazifist und politischer Autor

JEL Classification:
C00

A Data-driven Explainable Case-based Reasoning Approach for Financial Risk
Detection

Wei Li
Florentina Paraschiv
Georgios Sermpinis

Abstract:
The rapid development of artificial intelligence methods contributes to their
wide applications for forecasting various financial risks in recent years. This
study introduces a novel explainable case-based reasoning (CBR) approach without
a requirement of rich expertise in financial risk. Compared with other black-box
algorithms, the explainable CBR system allows a natural economic interpretation
of results. Indeed, the empirical results emphasize the interpretability of the
CBR system in predicting financial risk, which is essential for both financial
companies and their customers. In addition, results show that the proposed
automatic design CBR system has a good prediction performance compared to other
artificial intelligence methods, overcoming the main drawback of a standard CBR
system of highly depending on prior domain knowledge about the corresponding
field.

Keywords:
Case-based reasoning, Financial risk detection, Multiple-criteria decision-
making, Feature scoring, Particle swarm optimization, Parallel computing

JEL Classification:
C51, C52, C53, C61, C63, D81, G21, G32

Valuing cryptocurrencies: Three easy pieces

Michael C. Burda

Abstract:
This paper surveys the capacity of simple macroeconomic models — ”three easy
pieces” — to account for persistent and positive valuations of privately issued
assets based on the blockchain. Each of these three models — transactions demand
for a means of payment, consumption-based capital asset pricing, and search and
matching — highlights important aspects of digital payments. The mutual
interference of these jointly produced features may impede widespread use of
cryptocurrencies until technological innovations have been developed to separate
them.

JEL Classification:
C00

Correlation scenarios and correlation stress testing

Natalie Packham
Fabian Woebbeking

Abstract:
We develop a general approach for stress testing correlations of financial asset
portfolios. The correlation matrix of asset returns is specified in a parametric
form, where correlations are represented as a function of risk factors, such as
country and industry factors. A sparse factor structure linking assets and risk
factors is built using Bayesian variable selection methods. Regular calibration
yields a joint distribution of economically meaningful stress scenarios of the
factors. As such, the method also lends itself as a reverse stress testing
framework: using the Mahalanobis distance or highest density regions (HDR) on
the joint risk factor distribution allows to infer worst-case correlation
scenarios. We give examples of stress tests on a large portfolio of European and
North American stocks.

Keywords:
Correlation stress testing, reverse stress testing, factor selection, scenario
selection, Bayesian variable selection, market risk management

JEL Classification:
G11, G32

Penalized Weigted Competing Risks Models Based on Quantile Regression

Erqian Li
Wolfgang Karl Härdle
Xiaowen Dai
Maozai Tian

Abstract:
The proportional subdistribution hazards (PSH) model is popularly used to deal
with competing risks data. Censored quantile regression provides an important
supplement as well as variable selection methods, due to large numbers of
irrelevant covariates in practice. In this paper, we study variable selection
procedures based on penalized weighted quantile regression for competing risks
models, which is conveniently applied by researchers. Asymptotic properties of
the proposed estimators including consistency and asymptotic normality of non-
penalized estimator and consistency of variable selection are established. Monte
Carlo simulation studies are conducted, showing that the proposed methods are
considerably stable and efficient. A real data about bone marrow transplant
(BMT) is also analyzed to illustrate the application of proposed procedure.

Keywords:
Competing risks, Cumulative incidence function, Kaplan-Meier estimator,
Redistribution method

JEL Classification:
C00

Indices on Cryptocurrencies: an Evaluation

Konstantin Häusler
Hongyu Xia

Abstract:
Several cryptocurrency (CC) indices track the dynamics of the rising CC sector,
and soon ETFs will be issued on them. We conduct a qualitative and quantitative
evaluation of the currently existing CC indices. As the CC sector is not yet
consolidated, index issuers face the challenge of tracking the dynamics of a
fast-growing sector that is under continuous transformation. We propose several
criteria and various measures to compare the indices under review. Major
differences between the indices lie in their weighting schemes, their coverage
of CCs and the number of constituents, the level of transparency, and thus their
accuracy in mapping the dynamics of the CC sector. Our analysis reveals that
indices that adapt dynamically to this rising sector outperform their
competitors. Interestingly, increasing the number of constituents does not
automatically lead to a better fit of the CC sector. All codes are available on
Quantlet.com

Keywords:
Cryptocurrency, Index, Market Dynamics, Bitcoin

JEL Classification:
C00

Localizing Multivariate CAViaR

Yegor Klochkov
Wolfgang Karl Härdle
Xiu Xu

Abstract:
The risk transmission among financial markets is time-evolving, especially for
the extreme risk scenarios. The possibly sudden time variations of these risk
structures ask for quantitative technology that is able to cope with such
situations. Here we present a novel localized multivariate CAViaR-type model to
respond to the challenge of time-varying risk contagion. For this purpose a
local adaptive approach determines homogeneous intervals at each time point.
Critical values for this technique are calculated via multiplier bootstrap, and
the statistical properties of this ”localized multivariate CAViaR” are derived.
A comprehensive simulation study supports the effectiveness of our approach in
detecting structural change in multivariate CAViaR. Finally, when applying for
the US and German financial markets, we can trace out the dynamic tail risk
spillovers and find that the US market appears to play dominate role in risk
transmissions, especially in volatile market periods.

Keywords:
conditional quantile autoregression, local parametric approach, change point
detection, multiplier bootstrap

JEL Classification:
C32, C51, G17

High-dimensional Statistical Learning Techniques for Time-varying Limit Order
Book Networks

Shi Chen
Wolfgang Karl Härdle
Melanie Schienle

Abstract:
This paper provides statistical learning techniques for determining the full
own-price market impact and the relevance and effect of cross-price and cross-
asset spillover channels from intraday transactions data. The novel tools allow
extracting comprehensive information contained in the limit order books (LOB)
and quantify their impacts on the size and structure of price interdependencies
across stocks. For correct empirical network determination of such dynamic
liquidity price e ects even in small portfolios, we require high-dimensional
statistical learning methods with an integrated general bootstrap procedure. We
document the importance of LOB liquidity network spillovers even for a small
blue-chip NASDAQ portfolio.

Keywords:
limit order book, high-dimensional statistical learning, liquidity networks,
high frequency dynamics, market impact, bootstrap, network

JEL Classification:
C02, C13, C22, C45, G12