arXiv subjects

Till Massing

Publications and source records attributed to Till Massing.

11 recordsLinked to original sources

arXiv2024

Simulating Continuous-Time Autoregressive Moving Average Processes Driven By p-Tempered {\alpha}-Stable L\'evy Processes

We discuss simulation schemes for continuous-time autoregressive moving average (CARMA) processes driven by tempered stable L\'evy noises. CARMA processes are the continuous-time analogue of ARMA processes as well as a generalization of Ornstein-Uhlenbeck processes. However, unlike Ornstein-Uhlenbeck processes with a tempered stable driver (see, e.g., Qu et al. (2021)) exact transition probabilities for higher order CARMA processes are not explicitly given. Therefore, we follow the sample path generation method of Kawai (2017) and approximate the driving tempered stable L\'evy process by a truncated series representations. We derive a result of a series representation for ptempered {\alpha}-stable distributions extending Rosi\'nski (2007). We prove approximation error bounds and conduct Monte Carlo experiments to illustrate the usefulness of the approach.

math.PR↗

arXiv2023

On the parametric description of log-growth rates of cities' sizes of four European countries and the USA

We have studied the parametric description of the distribution of the log-growth rates of the sizes of cities of France, Germany, Italy, Spain and the USA. We have considered several parametric distributions well known in the literature as well as some others recently introduced. There are some models that provide similar excellent performance, for all studied samples. The normal distribution is not the one observed empirically.

econ.GN↗

arXiv2023

Student't mixture models for stock indices. A comparative study

We perform a comparative study for multiple equity indices of different countries using different models to determine the best fit using the Kolmogorov-Smirnov statistic, the Anderson-Darling statistic, the Akaike information criterion and the Bayesian information criteria as goodness-of-fit measures. We fit models both to daily and to hourly log-returns. The main result is the excellent performance of a mixture of three Student's $t$ distributions with the numbers of degrees of freedom fixed a priori (3St). In addition, we find that the different components of the 3St mixture with small/moderate/high degree of freedom parameter describe the extreme/moderate/small log-returns of the studied equity indices.

econ.GN↗

arXiv2023

Parametric Estimation of Tempered Stable Laws

Tempered stable distributions are frequently used in financial applications (e.g., for option pricing) in which the tails of stable distributions would be too heavy. Given the non-explicit form of the probability density function, estimation relies on numerical algorithms which typically are time-consuming. We compare several parametric estimation methods such as the maximum likelihood method and different generalized method of moment approaches. We study large sample properties and derive consistency, asymptotic normality, and asymptotic efficiency results for our estimators. Additionally, we conduct simulation studies to analyze finite sample properties measured by the empirical bias, precision, and asymptotic confidence interval coverage rates and compare computational costs. We cover relevant subclasses of tempered stable distributions such as the classical tempered stable distribution and the tempered stable subordinator. Moreover, we discuss the normal tempered stable distribution which arises by subordinating a Brownian motion with a tempered stable subordinator. Our financial applications to log returns of asset indices and to energy spot prices illustrate the benefits of tempered stable models.

math.ST↗

arXiv2023

A Data Mining Approach for Detecting Collusion in Unproctored Online Exams

Due to the precautionary measures during the COVID-19 pandemic many universities offered unproctored take-home exams. We propose methods to detect potential collusion between students and apply our approach on event log data from take-home exams during the pandemic. We find groups of students with suspiciously similar exams. In addition, we compare our findings to a proctored control group. By this, we establish a rule of thumb for evaluating which cases are "outstandingly similar", i.e., suspicious cases.

cs.CY↗

arXiv2023

Composite distributions in the social sciences: A comparative empirical study of firms' sales distribution for France, Germany, Italy, Japan, South Korea, and Spain

We study 17 different statistical distributions for sizes obtained {}from the classical and recent literature to describe a relevant variable in the social sciences and Economics, namely the firms' sales distribution in six countries over an ample period. We find that the best results are obtained with mixtures of lognormal (LN), loglogistic (LL), and log Student's $t$ (LSt) distributions. The single lognormal, in turn, is strongly not selected. We then find that the whole firm size distribution is better described by a mixture, and there exist subgroups of firms. Depending on the method of measurement, the best fitting distribution cannot be defined by a single one, but as a mixture of at least three distributions or even four or five. We assess a full sample analysis, an in-sample and out-of-sample analysis, and a doubly truncated sample analysis. We also provide the formulation of the preferred models as solutions of the Fokker--Planck or forward Kolmogorov equation.

econ.GN↗

arXiv2021

Approximation and Error Analysis of Forward-Backward SDEs driven by General L\'evy Processes using Shot Noise Series Representations

We consider the simulation of a system of decoupled forward-backward stochastic differential equations (FBSDEs) driven by a pure jump L\'evy process $L$ and an independent Brownian motion $B$. We allow the L\'evy process $L$ to have an infinite jump activity. Therefore, it is necessary for the simulation to employ a finite approximation of its L\'evy measure. We use the generalized shot noise series representation method by Rosinski (2001) to approximate the driving L\'evy process $L$. We compute the $L^p$ error, $p\ge2$, between the true and the approximated FBSDEs which arises from the finite truncation of the shot noise series (given sufficient conditions for existence and uniqueness of the FBSDE). We also derive the $L^p$ error between the true solution and the discretization of the approximated FBSDE using an appropriate backward Euler scheme.

math.PR↗

arXiv2021

Testing for Nonlinear Cointegration under Heteroskedasticity

This article discusses Shin (1994, Econometric Theory)-type tests for nonlinear cointegration in the presence of variance breaks. We build on cointegration test approaches under heteroskedasticity (Cavaliere and Taylor, 2006, Journal of Time Series Analysis) and nonlinearity, serial correlation, and endogeneity (Choi and Saikkonen, 2010, Econometric Theory) to propose a bootstrap test and prove its consistency. A Monte Carlo study shows the approach to have satisfactory finite-sample properties in a variety of scenarios. We provide an empirical application to the environmental Kuznets curves (EKC), finding that the cointegration test provides little evidence for the EKC hypothesis. Additionally, we examine a nonlinear relation between the US money demand and the interest rate, finding that our test does not reject the null of a smooth transition cointegrating relation

econ.EM↗

arXiv2021

When is the best time to learn? -- Evidence from an introductory statistics course

We analyze learning data of an e-assessment platform for an introductory mathematical statistics course, more specifically the time of the day when students learn. We propose statistical models to predict students' success and to describe their behavior with a special focus on the following aspects. First, we find that learning during daytime and not at nighttime is a relevant variable for predicting success in final exams. Second, we observe that good and very good students tend to learn in the afternoon, while some students who failed our course were more likely to study at night but not successfully so. Third, we discuss the average time spent on exercises. Regarding this, students who participated in an exam spent more time doing exercises than students who dropped the course before.

cs.CY↗

arXiv2021

Effects of Early Warning Emails on Student Performance

We use learning data of an e-assessment platform for an introductory mathematical statistics course to predict the probability of passing the final exam for each student. Subsequently, we send warning emails to students with a low predicted probability to pass the exam. We detect a positive but imprecisely estimated effect of this treatment, suggesting the effectiveness of such interventions only when administered more intensively.

cs.CY↗

arXiv2018

Towards digitalisation of summative and formative assessments in academic teaching of statistics

Web-based systems for assessment or homework are commonly used in many different domains. Several studies show that these systems can have positive effects on learning outcomes. Many research efforts also have made these systems quite flexible with respect to different item formats and exercise styles. However, there is still a lack of support for complex exercises in several domains at university level. Although there are systems that allow for quite sophisticated operations for generating exercise contents, there is less support for using similar operations for evaluating students' input and for feedback generation. This paper elaborates on filling this gap in the specific case of statistics. We present both the conceptional requirements for this specific domain as well as a fully implemented solution. Furthermore, we report on using this solution for formative and summative assessments in lectures with large numbers of participants at a big university.

cs.HC↗