On March 14th 2008 I defended my PhD thesis "Statistical
Analysis of Credit Risk - Topics in Default and Dependence Modelling" at the University of Oslo.
My PhD is part of a Strategic Institute Program
called Statistical Analysis of Risk at the Norwegian Computing Center and
the University of Oslo.
Below is some of the stuff I have been- and am currently working on.
Research Interests:
Financial risk management, Time series, Interest rate models, Dependency structures - copulas, Goodness-of-fit techniques
Publications:
D. Berg, J.-F. Quessy (2009)
Local power analysis of goodness-of-fit tests for copulas
Scandinavian Journal of Statistics 36, p. 389-412.
Abstract(HTML), Paper(PDF).
D. Berg (2009)
Copula Goodness-of-fit testing: An overview and power comparison
Forthcoming in The European Journal of Finance.
Abstract(HTML), Paper(PDF).
D. Berg, K. Aas (2009)
Models for construction of multivariate dependence: A comparison study
Forthcoming in The Europen Journal of Finance.
Abstract(HTML), Paper(PDF).
R. Dakovic, C. Czado, D. Berg (2009)
Bankruptcy prediction in Norway: a comparison study
Forthcoming in Applied Economic Letters.
Abstract(HTML), Paper(PDF).
D. Berg (2008)
Statistical Analysis of Credit Risk - Topics in Default and Dependence Modelling
Ph.D. thesis, University of Oslo.
Thesis(PDF).
D. Berg (2007)
Bankruptcy Prediction by Generalized Additive Models.
Applied Stochastic Models in Business and Industry 23(2), p. 129-143.
Abstract(HTML), Paper(PDF).
Working Papers:
D. Berg, H. Bakken (2007)
A copula goodness-of-fit approach based on the probability integral transformation.
Submitted.
Abstract(HTML), Paper(PDF).
Upcoming and past presentations:
The use of copulas - estimation, simulation, model choice/criticism. An applied introduction with examples in R/S-PLUS
20 November 2008 - Invited speach for the Norwegian ASTIN group.
Oslo, Norway. PDF
Models for construction of multivariate dependence
1 July 2008 - Invited speach at the 2nd R/Rmetrics User and Developer Workshop.
Meielisalp, Lake Thune, Switzerland. PDF
Copula goodness-of-fit testing: An overview and power comparison
16-19 June 2008 - Invited speach at the 22nd Nordic Conference on Mathematical Statistics.
Vilnius, Lithuania. PDF
Statistical Analysis of Credit Risk - Topics in Default and Dependence Modelling
14 March 2008 - Dissertation defense for the degree of Ph.D.
Oslo, Norway. PDF
Using and selecting among copulae: frequentist and Bayesian perspectives
14 March 2008 - Trial lecture for the degree of Ph.D.
Oslo, Norway. PDF
Copula goodness-of-fit testing: an overview and power comparison
14-15 September 2007 - Copulae and Multivariate Probability Distributions in Finance.
Warwick, UK. PDF
Models for construction of multivariate dependence
14-15 September 2007 - Copulae and Multivariate Probability Distributions in Finance.
Warwick, UK. PPT
Copula goodness-of-fit testing: an overview and power comparison
19-21 June 2007 - The 14th Norwegian meeting of statisticians.
Tromsoe, Norway. PDF
A copula goodness-of-fit approach based on the probability integral transform
24th April 2007 - Workshop on quantitative risk management.
Oslo, Norway. PDF
A copula goodness-of-fit approach based on the probability integral transform
24th November 2006 - Workshop on Copulas, Levy processes and Levy copulas.
Munich, Germany. PDF
A copula goodness-of-fit approach based on the probability integral transform
14th June 2006 - 21st Nordic Conference on Mathematical Statistics.
Rebild, Denmark. PDF
A copula goodness-of-fit approach based on the probability integral transform
19th May 2006 - International Conference on High Frequency Finance.
Konstanz, Germany. PDF
An introduction to copulae
14th March 2006 - Statistics seminar, NTNU.
Trondheim, Norway. PDF
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Abstracts:
D. Berg (2007)
Bankruptcy Prediction by Generalized Additive Models.
We compare several accounting based models for bankruptcy prediction.
The models are developed and tested on large data sets containing annual
financial statements for Norwegian limited liability firms. Out-of-sample
and out-of-time validation shows that generalized additive models significantly
outperform popular models like linear discriminant analysis, generalized linear
models and neural networks at all levels of risk. Further, important issues
like default horizon and performance depreciation are examined. We clearly see a
performance depreciation as the default horizon is increased and as time goes by.
Finally, a multi-year model, developed on all available data from three consecutive
years, is compared with a one-year model, developed on data from the most recent
year only. The multi-year model exhibit a desirable robustness to yearly fluctuations
that is not present in the one-year model.
Keywords: Bankruptcy Prediction, Generalized Additive Models, Default Horizon, Performance Depreciation, Multi-year model.
D. Berg, H. Bakken (2007)
A copula goodness-of-fit approach based on the conditional probability integral transform.
Goodness-of-fit testing for copulae recently emerged as a challenging
inferential problem and some approaches have been proposed. We
investigate such an approach based on the conditional probability
integral transformation. This approach implicitly weights observations at corners and edges of the
unit hypercube which makes it very powerful at detecting tail
heaviness for large sample sizes. However, it is shown
to perform rather poor for small sample sizes. We propose a generalization that
allows for any weighting, making it more robust and more powerful for
small sample sizes. Another weakness is that some
deviations from the null hypothesis may be neglected. We show an
example and propose an extension. The original approach is shown to be a special case of
our generalized and extended approach. Results from extensive Monte Carlo experiments
show that the our approach keeps prescribed levels well and that
certain weighting schemes produce superior power for three alternative
hypotheses and for various combinations of problem dimension and
sample size. The margins are treated as unknown nuisance parameters
and are replaced by their empirical distribution functions. In
addition, since we are testing a parametric null hypothesis requiring parameter
estimation, a parametric bootstrap procedure is required to
obtain reliable p-value estimates. Applied to daily log-returns of
collections of large cap stock portfolios the Gaussian- and
one-parameter Clayton- and Gumbel copulae are all strongly rejected,
increasingly so for increasing dimension and sample size. The
Student's t copula on the other hand, provides a good fit, indicating the presence of tail dependence in the daily log-returns of stock data.
Keywords: Copula, goodness-of-fit, conditional probability integral transformation, order statistic, parametric bootstrap.
D. Berg, K. Aas (2009)
Models for construction of multivariate dependence: A comparison study
In this article we review models for construction of higher-dimensional dependence
that have arisen recent years. A multivariate data set, which exhibit complex patterns of dependence,
particularly in the tails, can be modelled using a cascade of lower-dimensional copulae.
We examine two such models that differ in
their construction of the dependency structure, namely the nested Archimedean
constructions and the pair-copula constructions (also referred to as vines). The
constructions are compared, and estimation- and simulation techniques are examined.
The fit of the two constructions is tested on two different four-dimensional
data sets; precipitation values and equity returns, using a state of the art copula
goodness-of-fit procedure. The nested Archimedean construction is strongly rejected for both our data sets,
while the pair-copula construction provides an appropriate fit.
Through VaR calculations, we show that the latter does not overfit
data, but works very well even out-of-sample.
Keywords: Multivariate models, Nested Archimedean copulas, Pair-copula decompositions.
R. Dakovic, C. Czado, D. Berg (2009)
Bankruptcy prediction in Norway: A comparison study
In this paper we develop statistical models for bankruptcy prediction of Norwegian firms in the limited
liability sector using annual balance sheet information. We fit generalized linear-, generalized linear
mixed- and generalized additive models in a discrete hazard setting. It
is demonstrated that careful examination of the functional relationship
between the explanatory variables and the probability of bankruptcy
enhances the models' forecasting performance. Using information on
the industry sector we model the unobserved heterogeneity between
different sectors through an industry-specific random factor in the generalized linear mixed model.
The models developed in this paper are shown to outperform the model with Altman's variables at all levels
of risk. As a measure of models' forecasting accuracy the area under
the ROC curve is used.
Keywords:Bankruptcy Prediction, Industry Effects, Hazard Model, Generalized Linear Model, Generalized Linear Mixed Model, Generalized Additive Model
D. Berg, J.-F. Quessy (2009)
Local sensitivity analyses of goodness-of-fit tests for copulas
The asymptotic behavior of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Cram{\'e}r--von Mises functional of the empirical copula process and new moment-based goodness-of-fit statistics are made based on their associated asymptotic local power curves. It is shown that the choice of the estimator for the unknown parameter can have a significant influence on the power of the Cramer-von Mises test, and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods. The paper ends with an extensive simulation study that aims to extend the conclusions to small and moderate sample sizes.
Keywords: Asymptotic efficiency, contiguous alternatives, copula, Cramer-von Mises statistic, empirical copula process, goodness-of-fit, rank-based estimators
D. Berg (2009)
Copula goodness-of-fit testing: An overview and power comparison
Several copula goodness-of-fit approaches are examined, three of which are proposed
in this paper. Results are presented from an extensive Monte Carlo study, where we
examine the effect of dimension, sample size and strength of dependence on the nominal
level and power of the different approaches. While no approach is always the best, some
stand out and conclusions and recommendations are made. A novel study of p-value
variation due to permuation order, for approaches based on Rosenblatt’s transformation
is also carried out. Results show significant variation due to variable permutation for some
of the approaches based on this transform. However, when approaching critical/rejection
regions, the practical relevance of the additional variation is negligible.
Keywords: Copula, Cramer-von Mises statistic, empirical copula, goodness-of-fit, parametric bootstrap, pseudo-observations, Rosenblatt's transform
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