Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

Abstracts

IRTG 1792 DP Abstracts

IRTG1792DP2020 005

Targeting Cutsomers Under Response-Dependent Costs

Johannes Haupt
Stefan Lessmann

Abstract:
This study provides a formal analysis of the customer targeting decision problem
in settings where the cost for marketing action is stochastic and proposes a
framework to efficiently estimate the decision variables for campaign profit
optimization. Targeting a customer is profitable if the positive impact of the
marketing treatment on the customer and the associated profit to the company is
higher than the cost of the treatment. While there is a growing literature on
developing causal or uplift models to identify the customers who are impacted
most strongly by the marketing action, no research has investigated optimal
targeting when the costs of the action are uncertain at the time of the
targeting decision. Because marketing incentives are routinely conditioned on a
positive response by the customer, e.g. a purchase or contract renewal,
stochastic costs are ubiquitous in direct marketing and customer retention
campaigns. This study makes two contributions to the literature, which are
evaluated on a coupon targeting campaign in an e-commerce setting. First, the
authors formally analyze the targeting decision problem under response-dependent
costs. Profit-optimal targeting requires an estimate of the treatment effect on
the customer and an estimate of the customer response probability under
treatment. The empirical results demonstrate that the consideration of treatment
cost substantially increases campaign profit when used for customer targeting in
combination with the estimation of the average or customer- level treatment
effect. Second, the authors propose a framework to jointly estimate the
treatment effect and the response probability combining methods for causal
inference with a hurdle mixture model. The proposed causal hurdle model achieves
competitive campaign profit while streamlining model building. The code for the
empirical analysis is available on Github.

Keywords:
Heterogeneous Treatment Effect, Uplift Modeling, Coupon Targeting,
Churn/Retention, Campaign Profit

JEL Classification:
C00

IRTG1792DP2020 006

Forex exchange rate forecasting using deep recurrent neural networks

Alexander Jakob Dautel
Wolfgang Karl Härdle
Stefan Lessmann
Hsin‐Vonn Seow

Abstract:
Deep learning has substantially advanced the state of the art in computer
vision, natural language processing, and other fields. The paper examines the
potential of deep learning for exchange rate forecasting. We systematically
compare long short- term memory networks and gated recurrent units to
traditional recurrent network architectures as well as feedforward networks in
terms of their directional forecasting accuracy and the profitability of trading
model predictions. Empirical results indicate the suitability of deep networks
for exchange rate forecasting in general but also evidence the difficulty of
implementing and tuning corresponding architectures. Especially with regard to
trading profit, a simpler neural network may perform as well as if not better
than a more complex deep neural network.

Keywords:
Deep learning, Financial time series forecasting, Recurrent neural networks,
Foreign exchange rates

JEL Classification:
C14, C22, C45

IRTG1792DP2020 007

Deep Learning application for fraud detection in financial statements

Patricia Craja
Alisa Kim
Stefan Lessmann

Abstract:
Financial statement fraud is an area of significant consternation for potential
investors, auditing companies, and state regulators. Intelligent systems
facilitate detecting financial statement fraud and assist the decision-making of
relevant stakeholders. Previous research detected instances in which financial
statements have been fraudulently misrepresented in managerial comments. The
paper aims to investigate whether it is possible to develop an enhanced system
for detecting financial fraud through the combination of information sourced
from financial ratios and managerial comments within corporate annual reports.
We employ a hierarchical attention network (HAN) with a long short-term memory
(LSTM) encoder to extract text features from the Management Discussion and
Analysis (MD&A) section of annual reports. The model is designed to offer two
distinct features. First, it reflects the structured hierarchy of documents,
which previous models were unable to capture. Second, the model embodies two
different attention mechanisms at the word and sentence level, which allows
content to be differentiated in terms of its importance in the process of
constructing the document representation. As a result of its architecture, the
model captures both content and context of managerial comments, which serve as
supplementary predictors to financial ratios in the detection of fraudulent
reporting. Additionally, the model provides interpretable indicators denoted as
“red-flag” sentences, which assist stakeholders in their process of determining
whether further investigation of a specific annual report is required. Empirical
results demonstrate that textual features of MD&A sections extracted by HAN
yield promising classification results and substantially reinforce financial
ratios.

Keywords:
fraud detection, financial statements, deep learning, text analytics

JEL Classification:
C00

IRTG1792DP2020 008

Simultaneous Inference of the Partially Linear Model with a Multivariate Unknown
Function

Kun Ho Kim
Shih-Kang Chao
Wolfgang K. Härdle

Abstract:
In this paper, we conduct simultaneous inference of the non-parametric part of a
partially linear model when the non-parametric component is a multivariate
unknown function. Based on semi-parametric estimates of the model, we construct
a simultaneous confidence region of the multivariate function for simultaneous
inference. The developed methodology is applied to perform simultaneous
inference for the U.S. gasoline demand where the income and price variables are
contaminated by Berkson errors. The empirical results strongly suggest that the
linearity of the U.S. gasoline demand is rejected. The results are also used to
propose an alternative form for the demand.

Keywords:
Simultaneous inference, Multivariate function, Simultaneous confidence region,
Berkson error, Regression calibration

JEL Classification:
C12, C13, C14

IRTG1792DP2020 009

CRIX an Index for cryptocurrencies

Simon Trimborn
Wolfgang Karl Härdle

Abstract:
The cryptocurrency market is unique on many levels: Very volatile, frequently
changing market structure, emerging and vanishing of cryptocurrencies on a daily
level. Following its development became a difficult task with the success of
cryptocurrencies (CCs) other than Bitcoin. For fiat currency markets, the IMF
offers the index SDR and, prior to the EUR, the ECU existed, which was an index
representing the development of European currencies. Index providers decide on a
fixed number of index constituents which will represent the market segment. It
is a challenge to fix a number and develop rules for the constituents in view of
the market changes. In the frequently changing CC market, this challenge is even
more severe. A method relying on the AIC is proposed to quickly react to market
changes and therefore enable us to create an index, referred to as CRIX, for the
cryptocurrency market. CRIX is chosen by model selection such that it represents
the market well to enable each interested party studying economic questions in
this market and to invest into the market. The diversified nature of the CC
market makes the inclusion of altcoins in the index product critical to improve
tracking performance. We have shown that assigning optimal weights to altcoins
helps to reduce the tracking errors of a CC portfolio, despite the fact that
their market cap is much smaller relative to Bitcoin. The codes used here are
available via www.quantlet.de.

Keywords:
Index construction, Model selection, Bitcoin, Cryptocurrency, CRIX, Altcoin

JEL Classification:
C51, C52, G10

IRTG1792DP2020 010

Kernel Estimation: the Equivalent Spline Smoothing Method

Wolfgang K. Härdle
Michael Nussbaum

Abstract:
Among nonparametric smoothers, there is a well-known correspondence between
kernel and Fourier series methods, pivoted by the Fourier transform of the
kernel. This suggests a similar relationship between kernel and spline
estimators. A known special case is the result of Silverman (1984) on the
effective kernel for the classical Reinsch-Schoenberg smoothing spline in the
nonparametric regression model. We present an extension by showing that a large
class of kernel estimators have a spline equivalent, in the sense of identical
asymptotic local behaviour of the weighting coefficients. This general class of
spline smoothers includes also the minimax linear estimator over Sobolev
ellipsoids. The analysis is carried out for piecewise linear splines and
equidistant design.

Keywords:
Kernel estimator, spline smoothing, filtering coefficients, differential
operator, Green's function approximation, asymptotic minimax spline

JEL Classification:
C00

IRTG1792DP2020 011

The Effect of Control Measures on COVID-19 Transmission and Work Resumption:
International Evidence

Lina Meng
Yinggang Zhou
Ruige Zhang
Zhen Ye
Senmao Xia
Giovanni Cerulli
Carter Casady
Wolfgang K. Härdle

Abstract:
Many countries have taken non-pharmaceutical interventions (NPIs) to contain the
spread of the coronavirus (COVID-19) and push the recovery of national
economies. This paper investigates the effect of these control measures by
comparing five selected countries, China, Italy, Germany, the United Kingdom,
and the United States. There is evidence that the degree of early intervention
and efficacy of control measures are essential to contain the pandemic. China
stands out because its early and strictly enforced interventions are effective
to contain the virus spread. Furthermore, we quantify the causal effect of
different control measures on COVID-19 transmission and work resumption in
China. Surprisingly, digital contact tracing and delegating clear responsibility
to the local community appear to be the two most effective policy measures for
disease containment and work resumption. Public information campaigns and social
distancing also help to flatten the peak significantly. Moreover, material
logistics that prevent medical supply shortages provide an additional
conditioning factor for disease containment and work resumption. Fiscal policy,
however, is less effective at the early to middle stage of the pandemic.

Keywords:
COVID-19, coronavirus

JEL Classification:
C00

IRTG1792DP2020 012

On Cointegration and Cryptocurrency Dynamics

Georg Keilbar
Yanfen Zhang

Abstract:
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. A simple statistical arbitrage trading strategy is proposed showing a
great in-sample performance.

Keywords:
Cointegration, VECM, Nonstationarity, Cryptocurrencies

JEL Classification:
C00

IRTG1792DP2020 013

A Machine Learning Based Regulatory Risk Index for Cryptocurrencies

Xinwen Ni
Wolfgang Karl Härdle
Taojun Xie

Abstract:
Cryptocurrencies’ values often respond aggressively to major policy changes, but
none of the existing indices informs on the market risks associated with
regulatory changes. In this paper, we quantify the risks originating from new
regulations on FinTech and cryptocurrencies (CCs), and analyse their impact on
market dynamics. Specifically, a Cryptocurrency Regulatory Risk IndeX (CRRIX) is
constructed based on policy-related news coverage frequency. The unlabeled news
data are collected from the top online CC news platforms and further classified
using a Latent Dirichlet Allocation model and Hellinger distance. Our results
show that the machine-learning-based CRRIX successfully captures major policy-
changing moments. The movements for both the VCRIX, a market volatility index,
and the CRRIX are synchronous, meaning that the CRRIX could be helpful for all
participants in the cryptocurrency market. The algorithms and Python code are
available for research purposes on www.quantlet.de.

Keywords:
Cryptocurrency, Regulatory Risk, Index, LDA, News Classification

JEL Classification:
C45, G11, G18

IRTG1792DP2020 014

Cross-Fitting and Averaging for Machine Learning Estimation of Heterogeneous
Treatment Effects

Daniel Jacob

Abstract:
We investigate the finite sample performance of sample splitting, cross-fitting
and averaging for the estimation of the conditional average treatment effect.
Recently proposed methods, so-called meta- learners, make use of machine
learning to estimate different nuisance functions and hence allow for fewer
restrictions on the underlying structure of the data. To limit a potential
overfitting bias that may result when using machine learning methods, cross-
fitting estimators have been proposed. This includes the splitting of the data
in different folds to reduce bias and averaging over folds to restore
efficiency. To the best of our knowledge, it is not yet clear how exactly the
data should be split and averaged. We employ a Monte Carlo study with different
data generation processes and consider twelve different estimators that vary in
sample-splitting, cross-fitting and averaging procedures. We investigate the
performance of each estimator independently on four different meta-learners: the
doubly-robust-learner, R-learner, T-learner and X-learner. We find that the
performance of all meta-learners heavily depends on the procedure of splitting
and averaging. The best performance in terms of mean squared error (MSE) among
the sample split estimators can be achieved when applying cross-fitting plus
taking the median over multiple different sample-splitting iterations. Some
meta-learners exhibit a high variance when the lasso is included in the ML
methods. Excluding the lasso decreases the variance and leads to robust and at
least competitive results.

Keywords:
causal inference, sample splitting, cross-fitting, sample averaging, machine
learning, simulation study

JEL Classification:
C01, C14, C31, C63

IRTG1792DP2020 015

Tail-risk protection: Machine Learning meets modern Econometrics

Bruno Spilak
Wolfgang Karl Härdle

Abstract:
Tail risk protection is in the focus of the financial industry and requires
solid mathematical and statistical tools, especially when a trading strategy is
derived. Recent hype driven by machine learning (ML) mechanisms has raised the
necessity to display and understand the functionality of ML tools. In this
paper, we present a dynamic tail risk protection strategy that targets a maximum
predefined level of risk measured by Value-At-Risk while controlling for
participation in bull market regimes. We propose different weak classifiers,
parametric and non-parametric, that estimate the exceedance probability of the
risk level from which we derive trading signals in order to hedge tail events.
We then compare the different approaches both with statistical and trading
strategy performance, finally we propose an ensemble classifier that produces a
meta tail risk protection strategy improving both generalization and trading
performance.

Keywords:
-

JEL Classification:
C00

IRTG1792DP2020 025

Non-Parametric Estimation of Spot Covariance Matrix with High-Frequency Data

Konul Mustafayeva
Weining Wang

Abstract:
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.

Keywords:
high-frequency data; kernel estimation; jump; forecasting covariance matrix

JEL Classification:
C00

IRTG1792DP2020 024

Dynamic Spatial Network Quantile Autoregression

Xiu Xu
Weining Wang
Yongcheol Shin

Abstract:
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.

Keywords:
Network, Quantile autoregression, Instrumental variables, Dynamic models

JEL Classification:
C32, C51, G17

IRTG1792DP2020 023

The common and speci fic components of infl ation expectation across European
countries

Shi Chen
Wolfgang Karl Härdle
Weining Wang

Abstract:
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.

Keywords:
in ation expectation; joint yield-curve modeling; factor model; common trend;
spatial-temporal copulas

JEL Classification:
C02, C13, C38, E31, E43

IRTG1792DP2020 022

Tail Event Driven Factor Augmented Dynamic Model

Weining Wang
Lining Yu
Bingling Wang

Abstract:
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.

Keywords:
Quantile Regression, Expectile Regression, Dynamic Factor Model, Dynamic Network

JEL Classification:
C21, C51, G01, G18, G32, G38

IRTG1792DP2020 021

Improved Estimation of Dynamic Models of Conditional Means and Variances

Weining Wang
Jeffrey M. Wooldridge
Mengshan Xu

Abstract:
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.

Keywords:
-

JEL Classification:
C00

IRTG1792DP2020 020

Long- and Short-Run Components of Factor Betas: Implications for Stock Pricing

Hossein Asgharian
Charlotte Christiansen
Ai Jun Hou
Weining Wang

Abstract:
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.

Keywords:
long-run betas; short-run betas; risk premia; business cycles; component GARCH
model; MIDAS

JEL Classification:
G12; C58; C51

IRTG1792DP2020 019

Inference of breakpoints in high-dimensional time series

Likai Chen
Weining Wang
Wei Biao Wu

Abstract:
For multiple change-points detection of high-dimensional time series, we provide
asymptotic theory concerning the consistency and the asymptotic distribution of
the breakpoint statistics and estimated break sizes. The theory backs up a
simple two- step procedure for detecting and estimating multiple change-points.
The proposed two-step procedure involves the maximum of a MOSUM (moving sum)
type statistics in the rst step and a CUSUM (cumulative sum) re nement step on
an aggregated time series in the second step. Thus, for a xed time-point, we
can capture both the biggest break across di erent coordinates and aggregating
simultaneous breaks over multiple coordinates. Extending the existing high-
dimensional Gaussian approxima- tion theorem to dependent data with jumps, the
theory allows us to characterize the size and power of our multiple change-point
test asymptotically. Moreover, we can make inferences on the breakpoints
estimates when the break sizes are small. Our theoretical setup incorporates
both weak temporal and strong or weak cross-sectional dependence and is suitable
for heavy-tailed innovations. A robust long-run covariance matrix estimation is
proposed, which can be of independent interest. An application on detecting
structural changes of the U.S. unemployment rate is considered to illus- trate
the usefulness of our method.

Keywords:
multiple change points detection; temporal and cross-sectional dependence;
Gaussian approximation; inference of break locations

JEL Classification:
C00

IRTG1792DP2020 018

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