Seminar für Finanzökonometrie
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Dr. Fabian Spanhel

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Research interests

  • Dependence modeling
  • Inference for (vine) copulas and pair-copula constructions
  • Approximations based on the simplifying assumption
  • Partial dependence
  • Time series analysis
Preprints and publications
  1. M. S. Kurz and F. Spanhel. Testing the simplifying assumption in high-dimensional vine copulas. [Preprint 2017]
  2. F. Spanhel and M. S. Kurz. The partial vine copula: A dependence measure and approximation based on the simplifying assumption. [Preprint 2017]
    (A previous version of this paper was circulated under the title "F. Spanhel and M. S. Kurz. Simplified vine copula models: Approximations based on the simplifying assumption". [Preprint 2015])
  3. F. Spanhel and M. S. Kurz. The partial copula: Properties and associated dependence measures, Statistics & Probability Letters, Volume 119, December 2016, Pages 76-83. [http | Preprint 2015]
  4. C. Shellhase and F. Spanhel. Estimating non-simplified vine copulas using penalized splines, Statistics & Computing, February 2017, Pages 1-23. [http | Preprint 2016]
  5. F. Spanhel. Der Einfluss der Körpergröße auf Lohnhöhe und Berufswahl: Aktueller Forschungsstand und neue Ergebnisse auf Basis des Mikrozensus. WISTA – Wirtschaft und Statistik 02/2010, Statistisches Bundesamt. [http]


Selected talks
• 9th International Conference of the ERCIM Working Group on Computational and Methodological Statistics (CMStatistics 2016), University of Seville, Spain, December 9-11, 2016: “Modeling the serial dependence of financial returns with copulas”
• 6th CEQURA Conference on Advances in Financial and Insurance Risk, Munich, Germany, September 26-27, 2016: “Modeling the serial dependence of financial returns with copulas”
• Salzburg Workshop on Dependence Models & Copulas, University of Salzburg, Austria, September 19-22, 2016: “Modeling the serial dependence of financial returns with copulas”
• DAGStat 2016, University of Göttingen, Germany, March 14-18, 2016: “Simplified vine copula models: Approximations based on the simplifying assumption”
• 8th International Conference of the ERCIM Working Group on Computational and Methodological Statistics (CMStatistics 2015), Senate House & Birkbeck University of London, UK, December 12-14, 2015: “Simplified vine copula models: Approximations based on the simplifying assumption”
• Research Colloquium of the Department of Statistics, Ludwig-Maximilians-Universität München, Germany, December 9, 2015: “The curse of dimensions and simplified vine copula approximations”
• University of Bremen (invited by Martin Missong), Germany, November 2, 2015: “Modeling the serial dependence in (univariate) financial returns with copulas”
• University of Augsburg (invited by Yarema Okhrin), Germany, June 11, 2015: “Simplified vine copula models: Properties and testing”
• Technical University of Munich (invited by Claudia Czado), Germany, November 26, 2014: “Simplified vine copula approximations – Properties and consequences”
• International Workshop on High-Dimensional Dependence and Copulas: Theory, Modeling, and Applications, Beijing, China, January 3-5, 2014: “Copula Markov Duration Models”
• Statistische Woche 2013, Freie Universität Berlin, Germany, November 17-20, 2013: “Copula Markov Duration Models”
• SOFINE-CEQURA Spring Junior Workshop 2013 on Advances in Financial and Insurance Econometrics, Ebersberg, Germany, May 25-26, 2013: “Copula Markov Duration Models”
• 2nd CEQURA Conference on Advances in Financial and Insurance Risk, Munich, Germany, September 19-21, 2011: “Dependence Modeling with Mixture Copulas“
• DStatG-Nachwuchsworkshop, Leipzig, Germany, September 20, 2011: “Penalized Mixture of Copulas”

Abstracts

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Testing the simplifying assumption in high-dimensional vine copulas

(co-authored with Malte S. Kurz)

Abstract
Testing the simplifying assumption in high-dimensional vine copulas is a difficult task because tests must be based on estimated observations and amount to checking constraints on high-dimensional distributions. So far, corresponding tests have been limited to single conditional copulas with a low-dimensional set of conditioning variables. We propose a novel testing procedure that is computationally feasible for high-dimensional data sets and that exhibits a power that decreases only slightly with the dimension. By discretizing the support of the conditioning variables and incorporating a penalty in the test statistic, we mitigate the curse of dimensions by looking for the possibly strongest deviation from the simplifying assumption. The use of a decision tree renders the test computationally feasible for large dimensions. We derive the asymptotic distribution of the test and analyze its finite sample performance in an extensive simulation study. The utility of the test is demonstrated by its application to 10 data sets with up to 49 dimensions.

Keywords: Conditional copula, Pair-copula construction, Partial vine copula, Simplifying assumption,
Test for constant conditional correlation, Vine copula.

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The partial vine copula: A dependence measure and approximation based on the simplifying assumption

(co-authored with Malte S. Kurz)

Abstract
Simplified vine copulas (SVCs), or pair-copula constructions, have become an important tool in high-dimensional dependence modeling. So far, specification and estimation of SVCs has been conducted under the simplifying assumption, i.e., all bivariate conditional copulas of the vine are assumed to be bivariate unconditional copulas. We introduce the partial vine copula (PVC) which provides a new multivariate dependence measure and which plays a major role in the approximation of multivariate distributions by SVCs. The PVC is a particular SVC where to any edge a j-th order partial copula is assigned and constitutes a multivariate analogue of the bivariate partial copula. We investigate to what extent the PVC describes the dependence structure of the underlying copula. We show that the PVC does not minimize the Kullback-Leibler divergence from the true copula and that the best approximation satisfying the simplifying assumption is given by a vine pseudo-copula. However, under regularity conditions, step-wise estimators of pair-copula constructions converge to the PVC irrespective of whether the simplifying assumption holds or not. Moreover, we elucidate why the PVC is the best feasible SVC approximation in practice.

Keywords: Vine copula, Pair-copula construction, Simplifying assumption, Conditional copula, Approximation.
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The partial copula: Properties and associated dependence measures
(co-authored with Malte S. Kurz)

Abstract
The partial correlation coefficient is a commonly used measure to assess the conditional dependence between two random variables. We provide a thorough explanation of the partial copula, which is a natural generalization of the partial correlation coefficient, and investigate several of its properties. In addition, properties of some associated partial dependence measures are examined.

Keywords:  Partial copula, Conditional copula, Partial correlation, Partial Spearman’s rho, Partial
Kendall’s tau.
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Estimating non-simplified vine copulas using penalized splines
(co-authored with Christian Schellhase)

Abstract
Vine copulas (or pair-copula constructions) have become an important tool for high-dimensional dependence modeling. Typically, so called simplified vine copula models are estimated where bivariate conditional copulas are approximated by bivariate unconditional copulas. We present the first non-parametric estimator of a non-simplified vine copula that allows for varying conditional copulas. To overcome the curse of dimensionality, we approximate conditional copulas with more than one conditioning argument by a conditional copula with the first principal component as conditioning argument. Using penalized hierarchical B-splines we can directly estimate conditional copulas by setting linear restrictions on the spline coefficients. An extensive simulation study is conducted, showing a substantial improvement in the out-of-sample Kullback-Leibler divergence if the variation in the conditional copula is not negligible. An application to telescope data further demonstrates the potential benefit that can be achieved when conditional copulas are modeled.

Keywords: Vine, Pair-copula, Simplifying Assumption, Conditional Copula, Penalized Spline.
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Der Einfluss der Körpergröße auf Lohnhöhe und Berufswahl: Aktueller Forschungsstand und neue Ergebnisse auf Basis des Mikrozensus.

Abstract
Zahlreiche empirische Untersuchungen aus der internationalen Arbeitsmarktökonomik belegen einen ökonomisch bedeutenden Zusammenhang zwischen der Körpergröße eines Individuums und dessen erzielter Lohnhöhe. Noch wenig erforscht, aber genauso markant, sind die unterschiedlichen Körpergrößen von Personen in verschiedenen Berufsgruppen. Im Vordergrund dieser Studie steht zunächst die Frage, ob sich auch in den Daten des Mikrozensus ein statistisch und ökonomisch signifikanter Zusammenhang zwischen Körpergröße und Lohnhöhe nachweisen lässt und inwiefern sich der Effekt durch die Aufnahme von Kontrollvariablen erklären lässt.
Auf internationaler Ebene werden erstmals Indizien dafür gewonnen, dass die Lohndiskrepanz zwischen Männern unterschiedlicher Körpergröße mit steigender Berufserfahrung wächst.
Anschließend richtet sich der Fokus auf den Zusammenhang zwischen Körpergröße und Berufswahl – dieser wird ebenfalls das erste Mal für den deutschen Arbeitsmarkt erforscht.