Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG 1792 Discussion Paper 2018-001

Data Driven Value-at-Risk Forecasting using a SVR-GARCH-KDE Hybrid

Marius Lux
Wolfgang Karl Härdle
Stefan Lessmann


Abstract:
Appropriate risk management is crucial to ensure the competitiveness of financial institutions
and the stability of the economy. One widely used financial risk measure is Value-at-Risk
(VaR). VaR estimates based on linear and parametric models can lead to biased results or
even underestimation of risk due to time varying volatility, skewness and leptokurtosis of
nancial return series. The paper proposes a nonlinear and nonparametric framework to
forecast VaR. Mean and volatility are modeled via support vector regression (SVR) where
the volatility model is motivated by the standard generalized autoregressive conditional
heteroscedasticity (GARCH) formulation. Based on this, VaR is derived by applying kernel
density estimation (KDE). This approach allows for exible tail shapes of the profit and loss
distribution and adapts for a wide class of tail events.
The SVR-GARCH-KDE hybrid is compared to standard, exponential and threshold
GARCH models coupled with different error distributions. To examine the performance in
different markets, one-day-ahead forecasts are produced for different financial indices. Model
evaluation using a likelihood ratio based test framework for interval forecasts indicates that
the SVR-GARCH-KDE hybrid performs competitive to benchmark models. Especially models
that are coupled with a normal distribution are systematically outperformed.


Keywords: Value-at-Risk, Support Vector Regression, Kernel Density Estimation, GARCH

Nonparametric Variable Selection and Its Application to Additive Models


Zheng-Hui Feng
Lu Lin
Ruo-Qing Zhu
Li-Xing Zhu


Abstract:
For multivariate nonparametric regression models, existing variable selection
methods with penalization require high-dimensional nonparametric approximations
in objective functions. When the dimension is high, none of methods with penalization
in the literature are readily available. Also, ranking and screening approaches
cannot have selection consistency when iterative algorithms cannot be used due to
inefficient nonparametric approximation. In this paper, a novel and easily implemented
approach is proposed to make existing methods feasible for selection with
no need of nonparametric approximation. Selection consistency can be achieved.
As an application to additive regression models, we then suggest a two-stage procedure
that separates selection and estimation steps. An adaptive estimation to
the smoothness of underlying components can be constructed such that the consistency
can be even at parametric rate if the underlying model is really parametric.
Simulations are carried out to examine the performance of our method, and a real
data example is analyzed for illustration.


Keywords:
Adaptive estimation; non-parametric additive model; purely nonparametric
regression; variable selection

Systemic Risk in Global Volatility Spillover Networks: Evidence from Option-implied Volatility Indices


Zihui Yang
Yinggang Zhou


Abstract
With option-implied volatility indices, we provide a new tool for event studies in a network setting and document systemic risk in the spillover networks across global financial markets. Network linkages are sufficiently asymmetric because the US stock and bond markets play as dominant volatility suppliers to other countries and markets. Shocks from the US generate systemic risk through intensifying volatility spillovers across countries and asset classes. The findings offer new evidence that asymmetric network linkages can lead to sizable aggregate fluctuations and thus potential systemic risk.


Keywords:
Network; Option-implied Volatility; Spillover; Asymmetric linkage; Systemic risk

Pricing Cryptocurrency options: the case of CRIX and Bitcoin


Cathy YH Chen
Wolfgang Karl Härdle
Ai Jun Hou
Weining Wang


Abstract
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.


Keywords:
CRyptocurrency IndeX, CRIX, Bitcoin,Cryptocurrency, SVCJ, Option pricing,OCRIX

Testing for bubbles in cryptocurrencies with time-varying volatility Christian M. Hafner Abstract The recent evolution of cryptocurrencies has been characterized by bubble-like behavior and extreme volatility. While it is difficult to assess an intrinsic value to a specific cryptocurrency, one can employ recently proposed bubble tests that rely on recursive applications of classical unit root tests. This paper extends this approach to the case where volatility is time varying, assuming a deterministic longrun component that may take into account a decrease of unconditional volatility when the cryptocurrency matures with a higher market dissemination. Volatility also includes a stochastic short-run component to capture volatility clustering. The wild bootstrap is shown to correctly adjust the size properties of the bubble test, which retains good power properties. In an empirical application using eleven of the largest cryptocurrencies and the CRIX index, the general evidence in favor of bubbles is confirmed, but much less pronounced than under constant volatility. Keywords: cryptocurrencies, speculative bubbles, wild bootstrap, volatility JEL classification: C14, C43, Z11

A Note on Cryptocurrencies and Currency Competition

Anna Almosova


Abstract
The recent development of private cryptocurrencies has created a need to
extend existing models of private currency provision and currency competi-
tion. The outcome of cryptocurrency competition should be analyzed in a
model which incorporates important features of the modern cryptocurren-
cies. In this paper I focus on two such features. First, cryptocurrencies
operate according to a protocol - a blockchain - and are, therefore, free from
the time-inconsistency problem. Second, the operation of the blockchain
costs real resources. I use the Lagos-Wright search theoretic monetary model
augmented with privately issued currencies as in Fernandez-Villaverde and
Sanches (2016) and extend it by linear costs of private currency circulation. I
show that in contrast to Fernandez-Villaverde and Sanches (2016) cryptocur-
rency competition 1) does not deliver price stability and 2) puts downward
pressure on the in ation in the public currency only when the costs private
currency circulation (mining costs) are suciently low.


Keywords:
Currency competition, Cryptocurrency, In ation, Blockchain

JEL classication:
E40, E42, E50, E58

Knowing me, knowing you: inventor mobility and the formation of technology-oriented alliances

Stefan Wagner
Martin C. Goossen



Abstract
We link the hiring of R&D scientists from industry competitors to the subsequent formation of collaborative agreements, namely technology-oriented alliances. By transferring technological knowledge as well as cognitive elements to the hiring firm, mobile inventors foster the alignment of decision frames applied by potential alliance partners in the process of alliance formation thereby making collaboration more likely. Using data on inventor mobility and alliance formation amongst 42 global pharmaceutical firms over 16 years, we show that inventor mobility is positively associated with the likelihood of alliance formation in periods following inventor movements. This relationship becomes more pronounced if mobile employees bring additional knowledge about their prior firm’s technological capabilities and for alliances aimed at technology development rather than for agreements related to technology transfer. It is weakened, however, if the focal firm is already familiar with the competitor’s technological capabilities. By revealing these relationships, our study contributes to research on alliance formation, employee mobility, and organizational frames.


Keywords:


JEL classication:

A Monetary Model of Blockchain

Anna Almosova



Abstract
The recent emergence of blockchain-based cryptocurrencies has received a
considerable attention. The growing acceptance of cryptocurrencies has led
many to speculate that the blockchain technology can surpass a traditional
centralized monetary system. However, no monetary model has yet been de-
veloped to study the economics of the blockchain. This paper builds a model
of the economy with a single generally acepted blockchain-based currency. In
the spirit of the search and matching literature I use a matching function to
model the operation of the blockchain. The formulation of the money demand
is taken from a workhorse of monetary economics - Lagos and Wright (2005).
I show that in a blockchain-based monetary system money demand features
a precautionary motive which is absent in the standard Lagos-Wright model.
Due to this precautionary money demand the monetary equilibrium can be
stable for some calibrations. I also used the developed model to study how
the equilibrium return on money is

Keywords:
Blockchain, Miners, Cryptocurrency, Matching function

JEL classification:
E40, E41, E42

Deregulated day-ahead electricity markets in Southeast Europe: Price forecasting and comparative structural analysis

Antanina Hryshchuk
Stefan Lessmann



Abstract
Many Southeast European countries are currently undergoing a process of liberalization of electric power markets. The paper analyses day-ahead price dynamics on some of these new markets and in Germany as a benchmark of a completely decentralized Western European market. To that end, several price forecasting methods including autoregressive approaches, multiple linear regression, and neural networks are considered. These methods are tested on hourly day-ahead price data during four two-week periods corresponding to different seasons and varying levels of volatility in all selected markets. The most influential fundamental factors are determined and performance of forecasting techniques is analysed with respect to the age of the market, its degree of liberalization, and the level of volatility. A comparison of Southeast European electricity markets of different age with the older German market is made and clusters of similar Southeast European markets are identified.


Keywords:
ARIMA models, energy forecasting, time series models, neural networks

JEL classification:

How Sensitive are Tail-related Risk Measures in a Contamination Neighbourhood?

Wolfgang Karl Härdle
Chengxiu Ling



Abstract
Estimation or mis-specification errors in the portfolio loss distribution can have a considerable impact
on risk measures. This paper investigates the sensitivity of tail-related risk measures including
the Value-at-Risk, expected shortfall and the expectile-quantile transformation level in an epsiloncontamination
neighbourhood. The findings give the different approximations via the tail heaviness of
the contamination models and its contamination levels. Illustrating examples and an empirical study
on the dynamic CRIX capturing and displaying the market movements are given. The codes used to
obtain the results in this paper are available via https://github.com/QuantLet/SRMC


Keywords:
Sensitivity, expected shortfall, expectile, Value-at-Risk, risk management, influence function, CRIX

JEL classification:
C13, G10, G31

How to Measure a Performance of a Collaborative Research Centre

Alona Zharova
Janine Tellinger-Rice
Wolfgang Karl Härdle



Abstract
New Public Management helps universities and research institutions to perform in a highly competitive
research environment. Evaluating publicly financed research results improves transparency, helps in reflection
and self-assessment, and provides information for strategic decision making. In this paper we provide
empirical evidence using data from a Collaborative Research Centre (CRC) on financial inputs and research
output from 2005 to 2016. After selecting performance indicators suitable for a CRC, we describe main
properties of the data using visualization techniques. To study the relationship between the dimensions of
research performance, we use a time fixed effects panel data model and fixed effects Poisson model. With
the help of year dummy variables, we show how the pattern of research productivity changed over time after
controlling for staff and travel costs. The joint depiction of the time fixed effects and the research project’s
life cycle allows a better understanding of the development of the number of discussion papers over time.


Keywords:
Research Performance, Time Fixed Effects Panel Data Model, Fixed Effects Poisson Model, Network, Collaborative Research Centre

JEL classification:
C00

Targeting customers for profit: An ensemble learning framework to support marketing decision making

Stefan Lessmann
Kristof Coussement
Koen W. De Bock
Johannes Haupt



Abstract
Marketing messages are most effective if they reach the right customers. Deciding which customers
to contact is thus an important task in campaign planning. The paper focuses on empirical targeting
models. We argue that common practices to develop such models do not account sufficiently for
business goals. To remedy this, we propose profit-conscious ensemble selection, a modeling framework
that integrates statistical learning principles and business objectives in the form of campaign profit
maximization. The results of a comprehensive empirical study confirm the business value of the
proposed approach in that it recommends substantially more profitable target groups than several
benchmarks.


Keywords:
Marketing Decision Support, Business Value, Profit-Analytics, Machine Learning

JEL classification:
C00

Improving Crime Count Forecasts Using Twitter and Taxi Data

Lara Vomfell
Wolfgang Karl Härdle
Stefan Lessmann



Abstract
Data from social media has created opportunities to understand how and why
people move through their urban environment and how this relates to criminal
activity. To aid resource allocation decisions in the scope of predictive
policing, the paper proposes an approach to predict weekly crime counts. The
novel approach captures spatial dependency of criminal activity through approximating
human dynamics. It integrates point of interest data in the form
of Foursquare venues with Twitter activity and taxi trip data, and introduces a
set of approaches to create features from these data sources. Empirical results
demonstrate the explanatory and predictive power of the novel features. Analysis
of a six-month period of real-world crime data for the city of New York
evidences that both temporal and static features are necessary to eectively account
for human dynamics and predict crime counts accurately. Furthermore,
results provide new evidence into the underlying mechanisms of crime and give
implications for crime analysis and intervention.


Keywords:
Predictive Policing, Crime Forecasting, Social Media Data, Spatial Econometrics

JEL classification:
C00

Price Discovery on Bitcoin Markets

Paolo Pagnottoni
Dirk G. Baur
Thomas Dimpfl



Abstract
Trading of Bitcoin is spread about multiple venues where buying and selling is offered
in various currencies. However, all markets trade one common good and by the law of
one price, the different prices should not deviate in the long run. In this context we are
interested in which platform is the most important one in terms of price discovery. To this
end, we use a pairwise approach accounting for a potential impact of exchange rates. The
contribution to price discovery is measured by Hasbrouck's and Gonzalo and Granger's
information share. We then derive an ordering with respect to the importance of each
market which reveals that the Chinese OKCoin platform is the leader in price discovery
of Bitcoin, followed by BTC China.


Keywords:
price discovery; Bitcoin; Hasbrouck information shares;

JEL classification:
C58, C32, G23

Bitcoin is not the New Gold - A Comparison of Volatility, Correlation, and Portfolio Performance

Tony Klein
Hien Pham Thu
Thomas Walther


Abstract
Cryptocurrencies such as Bitcoin are establishing themselves as an investment asset and
are often named the New Gold. This study, however, shows that the two assets could
barely be more dierent. Firstly, we analyze and compare conditional variance properties
of Bitcoin and Gold as well as other assets and nd dierences in their structure.
Secondly, we implement a BEKK-GARCH model to estimate time-varying conditional
correlations. Gold plays an important role in nancial markets with ight-to-quality in
times of market distress. Our results show that Bitcoin behaves as the exact opposite
and it positively correlates with downward markets. Lastly, we analyze the properties of
Bitcoin as portfolio component and nd no evidence for hedging capabilities. We conclude
that Bitcoin and Gold feature fundamentally dierent properties as assets and linkages to
equity markets. Our results hold for the broad cryptocurrency index CRIX. As of now,
Bitcoin does not re ect any distinctive properties of Gold other than asymmetric response
in variance.


Keywords:
BEKK, Bitcoin, CRIX, Cryptocurrency, Gold, GARCH, Conditional Correlation, Asymmetry, Long memory

JEL classification:
C10; C58; G11

Time-varying Limit Order Book Networks

Wolfgang Karl Härdle
Shi Chen
Chong Liang
Melanie Schienle


Abstract
This paper analyzes the market impact of limit order books (LOB) taking crossstock
effects into account. Based on penalized vector autoregressive approach, we
aim to identify significance and magnitude of the directed network channels within
and between LOBs by bootstrapped impulse response functions. Moreover, information
on asymmetries and imbalances within the LOB over time would be derived. For
the sample of a NASDAQ blue-chip portfolio during 06-07/2016 we find that LOB
network effects crucially determine prices and bid-ask asymmetries are prevalent.


Keywords:
limit order book, high dimension, generalized impulse response, high frequency, market risk, market impact, network, bootstrap

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

Regularization Approach for Network Modeling of German Energy Market

Shi Chen
Wolfgang Karl Härdle
Brenda López Cabrera


Abstract
We investigate the concept of connectedness, which is important for risk
measurement and management inGerman energy market. Understanding and
learning from these mechanisms are essential to avoid future systemic disasters.
To deal with large portfolio selection, we propose regularization approach
to capture the spillover and contagion effects acrossGerman power derivatives.
This paper shows how network analysis can facilitate the monitoring of futures
price movements. Our methodology combines high-dimensional variable selection
techniques with network analysis, the results show that contracts like
Phelix Base Year Options and Phelix Peak Year Futures are in the core of the
Energy futures market.


Keywords:
regularization, energy risk transmission, network, German energy market

JEL classification:
C1, Q41, Q47

Adaptive Nonparametric Clustering

Kirill Efimov
Larisa Adamyan
Vladimir Spokoiny


Abstract
This paper presents a new approach to non-parametric cluster analysis
called Adaptive Weights Clustering (AWC). The idea is to identify the
clustering structure by checking at different points and for dierent scales
on departure from local homogeneity. The proposed procedure describes
the clustering structure in terms of weights wij each of them measures
the degree of local inhomogeneity for two neighbor local clusters using
statistical tests of \no gap" between them. The procedure starts from
very local scale, then the parameter of locality grows by some factor
at each step. The method is fully adaptive and does not require to
specify the number of clusters or their structure. The clustering results
are not sensitive to noise and outliers, the procedure is able to recover
dierent clusters with sharp edges or manifold structure. The method
is scalable and computationally feasible. An intensive numerical study
shows a state-of-the-art performance of the method in various articial
examples and applications to text data. Our theoretical study states
optimal sensitivity of AWC to local inhomogeneity.


Keywords:
adaptive weights, clustering, gap coecient, manifold clustering

JEL classification:

AMS 2000 Subject Classication:
Primary 62H30. Secondary 62G10

Lasso, knockoff and Gaussian covariates: a comparison


Laurie Davies


Abstract
Given data y and k covariates xj one problem in linear regression
is to decide which if any of the covariates to include when regressing
the dependent variable y on the covariates xj . In this paper three
such methods, lasso, knockoff and Gaussian covariates are compared
using simulations and real data. The Gaussian covariate method is
based on exact probabilities which are valid for all y and xj making
it model free. Moreover the probabilities agree with those based on
the F-distribution for the standard linear model with i.i.d. Gaussian
errors. It is conceptually, mathematically and algorithmically very
simple, it is very fast and makes no use of simulations. It outperforms
lasso and knockoff in all respects by a considerable margin.


Keywords:


JEL classification:

A Regime Shift Model with Nonparametric Switching Mechanism


Haiqiang Chen
Yingxing Li
Ming Lin
Yanli Zhu


Abstract
In this paper, we propose a new class of regime shift models with exible switching
mechanism that relies on a nonparametric probability function of the observed thresh-
old variables. The proposed models generally embrace traditional threshold models
with contaminated threshold variables or heterogeneous threshold values, thus gaining
more power in handling complicated data structure. We solve the identification issue by
imposing either global shape restriction or boundary condition on the nonparametric
probability function. We utilize the natural connection between penalized splines and
hierarchical Bayes to conduct smoothing. By adopting dierent priors, our procedure
could work well for estimations of smooth curve as well as discontinuous curves with
occasionally structural breaks. Bayesian tests for the existence of threshold eects are
also conducted based on the posterior samples from Markov chain Monte Carlo (M-
CMC) methods. Both simulation studies and an empirical application in predicting
the U.S. stock market returns demonstrate the validity of our methods.


Keywords:
Threshold Model, Nonparametric, Markov Chain Monte Carlo, Bayesian Inference, Spline.

JEL classification: