Prof. Dr. Jürgen Franke


Fraunhofer ITWM, Room E1.21
Fraunhofer-Platz 1
67663 Kaiserslautern

Contact Details

Tel.: +49 631 31600 4959


Consultation Hour

10:30 - 11:30 O `clock

Curriculum Vitae

1952 year of birth

4/1974 Diplom in Mathematics, Goethe-Universität Frankfurt a.M.

1974-1976  PhD grant, Studienstiftung des Deutschen Volkes

1976-1980 Research assistant, Goethe-Universität Frankfurt

2/1980 Dr. phil.nat., Goethe-Universität Frankfurt a.M.

1980-1981 Postdoctoral fellow, Goethe-Universität Frankfurt a.M.

1981-1982 Postdoctoral fellow, Special Research Center (SFB) 123, Ruprecht-Karls-Universität of Heidelberg

1982-1987 Hochschulassistent C1 (assistant professor), Goethe-Universität, Frankfurt a.M.

1/1985  Habilitation, Dept. of Mathematics, Goethe-Universität Frankfurt a.M.

1985 Research visitor at Australian National University, Canberra

1987-1988 Professor C3 for Applied Stochastics, Dept. of Mathematics, TU Berlin

1988-2017  Professor C4 (chair) for Applied Mathematical Statistics, Dept. of Mathematics, TU Kaiserslautern

1997 Research visitor at Humboldt Universität, Berlin

2000 Research visitor at Université Catholique de Louvain-la-neuve

2017- Consultant researcher, Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern

Research Interests

My mathematical research is focused on the development of models and estimation and testing methods for nonlinear time series, spatial data and stochastic processes from finance, risk management, material science and biomedical data analysis. The main topics are

  • local smoothing procedures, e.g. kernel estimates
  • wavelet-based function estimates
  • sieve estimates, e.g. neural networks or regression trees
  • functional data analysis for time series
  • resampling methods, mainly bootstrap variants, for confidence assessment of statistical inference.

My applied research in the Fraunhofer ITWM is concerned with applications of nonparametric statistics and machine learning to problems where generic machine learning methods fail due to lack of sufficient data and ignoring engineering knowledge about the processes involved.

Publikationen / Publications

J. Franke: Linear interpolation and prediction of time series with partially known spectral density and its relation to maximum entropy spectral estimation.

Proc. of the First ASSP Workshop on Spectral Estimation, McMaster University, Hamilton/Ontario (1981)


J. Franke: Optimal navigation with random terminal time in the presence of phase constraints.

Z. Wahrscheinlichkeitstheorie verw. Gebiete 60, 453-484 (1982)


J. Franke: The intuitive dynamic programming approach to optimal stochastic navigation.

Z. Wahrscheinlichkeitstheorie verw. Gebiete 60, 485-495 (1982)


J. Franke: Necessary conditions on optimal Markov controls for stochastic processes.

In: Stochastic Analysis and Applications, Advances in Probability, vol. 7, ed. M. Pinsky, Marcel Dekker, New York (1984)


J. Franke: On the robust prediction and interpolation of time series in the presence of correlated noise.

J. Time Ser. Analysis 5, 227-244 (1984)


J. Franke, V.H. Poor: Minimax-robust filtering and finite-length robust predictors.

In: Robust and Nonlinear Time Series Analysis, eds. J. Franke, W. Härdle, R.D. Martin, Lecture Notes in Statistics 26, Springer, Berlin-Heidelberg-New York (1984)


J. Franke: Minimax-robust prediction of discrete time series.

Z. Wahrscheinlichkeitstheorie verw. Gebiete 68, 337-364 (1985)


H. Steinberg, J. Franke and Th. Gasser: Fitting autoregressive processes to EEG time series: an empirical comparison of estimates of the order (mit Th. Gasser und H. Steinberg).

IEEE Trans. on Acoustics, Speech and Signal Processing 33, 143-150 (1985)


J. Franke: A Levinson-Durbin recursion for autoregressive-moving average processes.

Biometrika 72, 573-581 (1985)


J. Franke: ARMA processes have maximal entropy among time series with prescribed autocovariances and impulse responses.

Adv. Appl. Prob. 17, 810-840 (1985)


J. Franke: A recursive-in-order algorithm for estimating ARMA-parameters.

Statistics and Decisions, Suppl. Issue 2, 309-313 (1985)


J. Franke, M. Wendel: A bootstrap approach for nonlinear autoregressions - some preliminary results.

In: Bootstrapping and Related Techniques, eds. K.-H. Jäckel, G. Rothe, W. Sendler, Lecture Notes in Economics and Mathematical Systems 376, Springer, Berlin-Heidelberg-New York (1990)


J. Franke: An improved version of Breiman's minimax filter.

Note Mat. 11, 157-175 (1991)


J. Franke, B. Gründer: Stochastic modelling for analyzing immission data in forests.

In: Tagungsberichte der AG Biometrie in der Ökologie der deutschen Region der Biometrischen Gesellschaft, Heft 3 (1992)


J. Franke, J.-P. Kreiß: Bootstrapping ARMA-models.

J. Time Ser. Analysis 13, 297-317 (1992)


J. Franke, W. Härdle: On bootstrapping kernel spectrum estimates.

Ann. Statist. 20, 121-145 (1992)


J. Franke, Th. Seligmann: Conditional maximum likelihood estimates for INAR(1)-models and their application to modelling epileptic seizure counts.

In: Developments in Time Series Analysis, ed. T. Subba Rao, Chapman & Hall (1993)


J. Franke, B. Gründer: General kriging for spatial-temporal processes with random ARX-regression parameters.

In: Time Series Analysis - In memory of E.J. Hannan, ed. P.M. Robinson und M. Rosenblatt, Lecture Notes in Statistics 115, Springer, Berlin-Heidelberg-New York (1996)


J. Franke, K. Han and Y. T. Feng: Numerical methods of generating random points with prescribed distributional properties in (non)rational Bezier surfaces.

Math. Comp. Modelling 23, 15-28 (1996).


J. Franke: Nonlinear and nonparametric methods for analyzing financial time series

In OR ‘98, ed. P. Kall et al., Springer, Berlin-Heidelberg-New York 1999


J. Franke, M. Neumann: Bootstrapping neural networks.

Neural Computation 12, 1929-1949 (2000)


J. Franke: Portfolio Management and Market Risk Quantification using Neural Networks. In: Statistics and Finance: An Interface, W.S. Chan, W.K. Li and H. Tong eds., Imperial College Press, London 2000


V. Delouille, J. Franke and R. von Sachs: Nonparametric stochastic regression with design-adapted wavelets (mit V. Delouille und R. von Sachs)

Sankhya Ser. A 63, 328-366 (2001)


J. Franke, J.-P. Kreiß and E. Mammen: Bootstrap of kernel smoothing in nonlinear time series.

Bernoulli 8, 1-37 (2002).


J. Franke, J.-P. Kreiß, E. Mammen and M. Neumann: Properties of the nonparametric autoregressive bootstrap.

Journal of Time Series Analysis 23, 555-585 (2002)


H. Holzberger, J. Franke and M. Müller:  Nonparametric estimation of GARCH-processes.

In: Applied Quantitative Finance, W. Härdle, Th. Kleinow, G. Stahl eds., Springer,

Berlin-Heidelberg-New York (2002)


J. Franke, G. Kroisandt: Nonparametric changepoint detection for time series.

PAMM 2, 456-458 (2003)


J. Franke, W. Härdle and J.-P. Kreiß: Nonparametric estimation in a stochastic volatility model.

In: Recent Advances and Trends in Nonparametric Statistics. eds. M. Akritas and D. N. Politis, Elsevier, North Holland (2003)


J. Franke, M. Neumann and J.-P. Stockis: Bootstrapping nonparametric estimators of the volatility function.

Journal of Econometrics 118, 189-218 (2004)


J. Franke, M. Diagne and P. Mwita: Nonparametric value-at-risk estimates.

Oberwolfach Reports 1, 133-134 (2004)


U. Wunn, M. Bücking, J. Franke and A. Roeder Sequentielle Multihypothesentests zur Bestimmung von Gefährdungsstufen bei Schalenwildverbiss im Rahmen der Erstellung waldbaulicher Gutachten - ein neuer Verfahrensansatz (mit)

Allgemeine Forst- und Jagdzeitung 175, 239-244 (2004)


P. Mwita, R. Odhiambo, A. Waititu Gichuhi and J. Franke:Direct Conditional Quantiles: Kernel Estimator and its Consistency.

African Journal of Science and Technology 6, 67-76 (2005)


J. Franke, J. Löhr: On the identification of large multilinear systems.

Computational Statistics 21, 415-429 (2006)


J. Franke, M. Diagne:Estimating market risk with neural networks.

Statistics and Decisions 24, 233-253 (2006)


J. Franke, J.-P. Kreiß and M. Moser: Bootstrap autoregressive order selection.

Statistics and Decisions 24, 305-325 (2006)


A. Sarishvili, C. Andersson, J. Franke and G. Kroisandt: On the consistency of the blocked neural network estimator in time series analysis.

Neural Computation 18, 2568 - 2581 (2006)


P. Mwita, J. Franke:Estimation of Critical Streamflow Discharge Level using Quantile Regression Approach.

In: Proceedings of the IASTED Conference on Modelling, Simulation and Optimization, ed. H. Nyongesa, 2006


J. Franke, S. Halim: Wild bootstrap tests for signals and images.

IEEE Signal Processing Magazine 24, no. 4, 31-37 (2007)


J. Franke, J.-P. Stockis and J. Tadjuidje Kamgaing: Sieve Estimates for Conditional Quantiles of Financial Time Series.

Oberwolfach Reports 4, 860-861 (2007)


J. Franke, J.-P. Stockis and J. Tadjuidje Kamgaing: A note on the identifiability of the conditional expectation for the mixtures of neural networks.

Statistics and Probab. Letters 78, 739-742 (2008)


J. Franke, J.-P. Stockis and J. Tadjuidje Kamgaing: On geometric ergodicity of CHARME models.

J. Time Ser. Analysis 31, 141-152 (2010)


J. Franke, J.-P. Stockis, J. Tadjuidje Kamgaing and W.K. Li: Mixtures of nonparametric autoregressions.

J. Nonparametric Statistics 23, 287-303 (2011)


J. Franke, C. Kirch and J. Tadjuidje Kamgaing: Changepoints in Times Series of Counts.

J. Time Ser. Analysis 33, 757-770 (2012)


A. Waititu Gichuhi, J.M. Kihoro and J. Franke: Parametric changepoint estimation, testing and confidence intervals applied to business.

J. Agricultural Science and Technology 14, 136-148 (2012)


M. Fiecas, J. Franke, R. von Sachs and J. Tadjuidje Kamgaing: Stable Estimates for High dimensional Hidden Markov Models.

Oberwolfach Report  48, 18-21 (2013).


F. Kramer, D. Griesemer, D. Bakker, S. Brill, E. Frotscher, J. Franke and E. Friauf: Inhibitory glycinergic neurotransmission in the mammalian auditory brainstem upon prolonged stimulation: short-term plasticity and synaptic reliability.

Front. Neural Circuits 8: 14, doi:  10.3389/fncir.2014.00014 (2014)


J. Franke, P. Mwita and W. Wang: Nonparametric Estimates of Conditional Quantiles for Time Series.

AStA Adv. Stat. Anal. 99, 107-130 (2015)


J. Franke, C. Redenbach and N. Zhang: On a mixture model for directional data on the sphere.

Scand. Journal of Statistics 43, 139-155 (2016)


E. G. Krächan, A. U. Fischer, J. Franke and E. Friauf: Synaptic reliability and temporal precision are achieved via high quantal content and effective replenishment: auditory brainstem versus hippocampus.

Journal of Physiology 595, 839-864 (2017)


P. Ruckdeschel, C. Erlwein-Sayer, J. Franke and E. Massini: Methode zur Berechnung eines Garantieschadens als sichere untere Schranke für den Gesamtschaden.

Zeitschrift für Medizinstrafrecht 3, 67-79 (2017)


M. Fiecas, J. Franke, R. von Sachs and J. Tadjuidje Kamgaing: Shrinkage for multivariate hidden Markov models.

JASA 112, 424-435 (2017)

J. Franke, W. Härdle and Ch. Hafner: Statistik der Finanzmärkte

Springer,  Berlin-Heidelberg-New York (1. Auflage, 2001; 2. ergänzte Auflage, 2003)


J. Franke, W. Härdle and Ch. Hafner: Statistics of Financial Markets

Springer,  Berlin-Heidelberg-New York (1. Auflage, 2004; 2. ergänzte Auflage, 2008, 3. ergänzte Auflage, 2011, 4. ergänzte Auflage, 2015)


J. Franke, W. Härdle and Ch. Hafner:  金融教材译丛·金融计量:金融市场统计分析

Mechanical Industry Press and Springer. Chinese translation of Statistics of Financial Markets: an Introduction (2017)


J. Franke:Time Series Analysis. In: Encyclopaedia of Actuarial Science, eds. B. Sundt und J. Teugels. Wiley, New York (2004)


J. Franke and numerous co-authors: Structural Adaptive Smoothing Procedures.

In: Mathematical Methods in Signal Processing and Digital Image Processing, eds. R. Dahlhaus, J. Kurths, P. Maaß and J. Timmer, pp. 183-229, Springer, Berlin-Heidelberg-New York (2008)


J. Franke, J.-P. Kreiß and E. Mammen: Nonparametric Modelling in Financial Time Series.

In: Handbook of Financial Time Series, eds. T.G. Andersen, R.A. Davis, J.P. Kreiß and T. Mikosch. Springer, Berlin-Heidelberg-New York (2009).


J. Franke:Markov Switching Time Series Models.

In: Handbook of Statistics - vol 30.  Time  Series - Methods and Applications, eds. C.R. Rao and T. Subba Rao, Elsevier B.V., Amsterdam, p. 99-122 (2012)


J. Franke, P. Lang:Datenanalyse.

In: Mathematik im Fraunhofer-Institut, eds. H. Neunzert und D. Prätzel-Wolters, Springer, Berlin-Heidelberg-New York, p. 65-83 (2014)


J. Franke, P. Lang:Data Analysis.

In: Currents in Industrial Mathematics, eds. H. Neunzert und D. Prätzel-Wolters, Springer, Berlin-Heidelberg-New York, p. 65-82 (2015)

J. Franke, W. Härdle and R.D. Martin:  Robust and Nonlinear Time Series Analysis.

Lecture Notes in Statistics 26, Springer, Berlin-Heidelberg-New York (1984)

(zusammen mit W. Härdle und R.D. Martin)


J. Franke, A. Roeder:Mathematical Modelling of Forest Ecosystems.

J. D. Sauerländer's Verlag, Frankfurt (1992)


J. Franke, W. Härdle and G. Stahl: Measuring Risk in Complex Stochastic Systems.

Lecture Notes in Statistics 47, Springer, Berlin-Heidelberg-New York (2000)

Th. Gasser, J. Franke and H. Steinberg: On a goodness-of-fit test for spectral densities and its application to autoregressive spectral estimates.

Preprint 237, SFB 123 Stochastische Mathematische Modelle, Heidelberg, 1983


J. Franke: On multivariate robust Wiener filters.

Preprint 363, SFB 123 Stochastische Mathematische Modelle, Heidelberg, 1986


J. Franke, G. Gleichmann:  Automatic generation of sleep profiles from the electroencephalogram - a pilot study.

Preprint 376, SFB 123 Stochastische Mathematische Modelle, Heidelberg, 1986


J. Franke, T. Subba Rao: Multivariate first-order integer-valued autoregressions (mit T. Subba Rao).

Report in Technomathematik 95,TU Kaiserslautern, 1993


J. Franke, E. Valenzuela-Dominguez: A Bernstein inequality for strongly mixing spatial random processes.

DFG-SPP 1114 Preprint 76 (2005)


J. Franke, S. Halim: A bootstrap test for comparing images in surface inspection.

DFG-SPP 1114 Preprint 150 (2006)


S. Feth, J. Franke and M. Speckert: Resampling-Methoden zur mse-Korrektur und Anwendungen in der Betriebsfestigkeit.

Berichte des Fraunhofer ITWM 116 (2007)


J. Franke, J.-P. Stockis and J. Tadjuidje Kamgaing: Quantile Sieve Estimates for Time Series. Report in Wirtschaftsmathematik 105, TU Kaiserslautern  (2007)


J. Franke, S. Didas, J. Tadjuidje Kamgaing and J. Weickert: Some asymptotics for local least-squares regression with regularization.

Report in Wirtschaftsmathematik 107, TU Kaiserslautern (2007)


J. Franke, J. Tadjuidje Kamgaing: Maximum Likelihood Estimators for Markov Switching Autoregressive Processes with ARCH Component.

Report in Wirtschaftsmathematik 124, TU Kaiserslautern, 2009


J. Franke, J.T.N. Krebs and E. Valenzuela-Dominguez: A Bernstein inequality for spatial lattice processes.

arXiv:1702.02023 [math.ST], 2017


J. Franke, E. G. Nyarige and A. Fischer: On Changepoint Detection in a Series of Stimulus-Response Data.

Report in Wirtschaftsmathematik 165 (urn:nbn:de:hbz:386-kluedo-51399), TU Kaiserslautern, 2018



J. T. N. Krebs and J. Franke: The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series.

arXiv:1811.06172 [math.ST], 2018


J. Franke and E. G. Nyarige: A residual-based bootstrap for functional autoregressions.

arXiv:1905.07635 [math.ST], 2019