MARKET RISK MODEL IDENTIFICATION AND VALIDATION USING NOVEL STATISTICAL, PROBABILISTIC, AND MACHINE LEARNING TOOLS

    Grant no.: 2020/37/B/HS4/00120 (OPUS)

    Funding agency: National Science Centre (NCN), Poland

    Funding period: 14.01.2021-13.01.2025

    Partners: Jagiellonian University (M. Pitera), Polish Academy of Science (Ł. Stettner), Wrocław University of Science and Technology (A. Wyłomańska)

    Total budget: 396 732 PLN

    Tasks

    1. Model identification/validation based on conditional quantile moments analysis
    2. Novel risk and performance quantification methods
    3. Long-run stochastic equilibrium analysis in finance

    Selected publications

    1. H. Woszczek, A. Chechkin, A. Wyłomańska: Scaled Brownian motion with random anomalous diffusion exponent, Communications in Nonlinear Science and Numerical Simulation 140(1), 108388, 2025
    2. A. Pacheco-Pozo, M. Balcerek, A. Wyłomańska, K. Burnecki, I. M. Sokolov, D. Krapf: Langevin equation in heterogeneous landscapes: how to choose the interpretation, Phys. Rev. Lett. 133, 067102, 2024
    3. A. M. Sathe, N. S. Upadhye, A. Wyłomańska: Forecasting multidimensional autoregressive time series model with symmetric alpha-stable noise using artificial neural networks, Statistical Methods & Applications 33, 783–805, 2024
    4. K. Pączek, D. Jelito, M. Pitera, A. Wyłomańska: Goodness-of-fit tests for the one-sided Levy distribution based on quantile conditional moments, Journal of Applied Statistics 1–24, 2024, https://doi.org/10.1080/02664763.2024.2340592
    5. K. Pączek, D. Jelito, M. Pitera, A. Wyłomańska: Estimation of stability index for symmetric alpha-stable distribution using quantile conditional variance ratios, TEST 33, 297–334, 2024
    6. A. Grzesiek, J. Gajda, S. Thapa, A. Wyłomańska: Distinguishing between fractional Brownian motion with random and constant Hurst exponent using sample autocovariance-based statistics, Chaos 34, 043154, 2024
    7. J. Janczura, A. Puć, Ł. Bielak, A. Wyłomańska: Product of bi-dimensional VAR(1) model components. An application to the cost of electricity load prediction errors Statistics & Risk Modeling 41 (1/2) 1-26, 2024
    8. M. Balcerek, A. Wyłomańska, K. Burnecki, R. Metzler, D. Krapft: Modelling intermittent anomalous diffusion with switching fractional Brownian motion, New J. Phys. 25 103031, 2023
    9. H. Woszczek, A. Wyłomańska: Autoregressive model with double Pareto distributed noise, Mathematica Applicanda 51(1), 121-141, 2023
    10. W. Wang, M. Balcerek, K. Burnecki, A. V. Chechkin, S.Janusonis, J. Ślęzak, T. Vojta, A. Wyłomańska, and R. Metzler: Memory-multi-fractional Brownian motion with continuous correlations, Phys. Rev. Research 5, L032025, 2023
    11. K. Maraj-Zygmąt, A. Grzesiek, G. Sikora, J. Gajda, A. Wyłomańska: Testing of two-dimensional Gaussian processes by sample cross-covariance function, Chaos 33, 073135, 2023
    12. M. Dhull, A. Kumar, A. Wyłomańska: The expectation-maximization algorithm for autoregressive models with normal inverse Gaussian innovations, Communications in Statistics - Simulation and Computation, 1-21, 2023, https://doi.org/10.1080/03610918.2023.2186334
    13. J. Gajda, A. Grzesiek, A. Wyłomańska: Ornstein - Uhlenbeck process driven by alpha-stable process and its Gamma subordination, Methodology and Computing in Applied Probability 25,9, 2023
    14. K. Maraj-Zygmąt, G. Sikora, M. Pitera, A. Wyłomańska: Goodness-of-fit test for stochastic processes using even empirical moments statistic, Chaos 33, 013128, 2023
    15. A. M. Sathe, N. S. Upadhye, A. Wyłomańska: Forecasting of symmetric alpha-stable autoregressive models by time series approach supported by artificial neural networks, Journal of Computational and Applied Mathematics 425, 115051, 2023
    16. J. Adamska, L. Bielak, J. Janczura, A. Wyłomańska: From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t-Distribution Case, Mathematics 10(18), 3371, 2021
    17. M. Balcerek, K. Burnecki, S. Thapa, A. Wyłomańska, A. Chechkin: Fractional Brownian motion with random Hurst exponent: accelerating diffusion and persistence transitions, Chaos 32, 093114, 2022
    18. D. Szarek, I. Jabłoński, D. Krapf, A. Wyłomańska: Multifractional Brownian motion characterization based on Hurst exponent estimation and statistical learning, Chaos 32, 083148, 2022
    19. D. Szarek, K. Maraj-Zygmąt, G. Sikora, D. Kraft, A. Wyłomańska: Statistical test for anomalous diffusion based on empirical anomaly measure for Gaussian processes, Computational Statistics & Data Analysis 168, 107401, 2022
    20. Ł. Bielak, A. Grzesiek, J. Janczura, A. Wyłomańska: Market risk factors analysis for an international mining company. Multi-dimensional heavy-tailed-based modelling, Resources Policy 74, 102308, 2021
    21. A. Grzesiek, M. Mrozinska, P. Giri, S. Sundar, A. Wyłomańska: The covariation-based Yule-Walker method for multidimensional autoregressive time series with alpha-stable distributed noise , Int J Adv Eng Sci Appl Math 13, 13, 394–414, 2021
    22. P. Giri, S. Sundar, A. Wyłomańska: Fractional lower order covariance (FLOC) based estimation for multidimensional PAR(1) model with alpha−stable noise, Int J Adv Eng Sci Appl Math 13, 215–235, 2021
    23. M. Markiewicz, A. Wyłomańska: Time series forecasting - problem of heavy-tailed distributed noise, Int J Adv Eng Sci Appl Math 13, 248–256, 2021
    24. K. Maraj, D. Szarek, G. Sikora, A. Wyłomańska: Time averaged mean squared displacements ratio test for Gaussian processes with unknown diffusion coefficient, Chaos 31, 073120, 2021
    25. M. Balcerek, K. Burnecki, G. Sikora, A. Wyłomańska: Discriminating Gaussian processes via quadratic form statistics, Chaos 31, 063101, 2021

NonGaussMech - NEW METHODS OF PROCESSING NON-STATIONARY SIGNALS (IDENTIFICATION, SEGMENTATION, EXTRACTION, MODELING) WITH NON-GAUSSIAN CHARACTERISTICS FOR THE PURPOSE OF MONITORING COMPLEX MECHANICAL STRUCTURES

    Grant no.: 2021/40/Q/ST8/00024 (SHENG)

    Funding agency: National Science Centre (NCN), Poland

    Funding period: 1.02.2022-31.01.2025

    Partners: Tsinghua University, Beijing (China); Faculty of Pure and Applied Mathematics (WMat) WUST (Poland); Faculty of Geoengineering, Mining and Geology (WGGG) WUST (Poland)

    Total budget: 414 842 EUR

    A key personnel consists of: prof. Fulei Chu (Tsinghua University), prof. Agnieszka Wyłomańska (WMat), prof. Radoslaw Zimroz (WGGG/KG/DMC).

    Research team (WUST)

    1. Radosław Zimroz
    2. Agnieszka Wyłomańska
    3. Mateusz Gabor (Ph.D. student)
    4. Katarzyna Skowronek (Ph.D. student)
    5. Wojciech Żuławiński (Ph.D. student)
    6. Daniel Kuzio (Ph.D. student)

    Tasks

    1. Impulsive noise modeling and nonstationary operational condition parametrisation
    2. Hidden Cyclicity/Periodicity detection (in case of non-existing second-order statistics)
    3. Multidimensional data processing algorithms for impulsive sources separation and signal of interest extraction

    Selected publications

    1. D. Kuzio, R. Zimroz, A. Wyłomańska: A procedure for assessing of machine health index data prediction quality, Measurement 240, 116040, 2025
    2. J. Janczura, W. Żuławiński, H. Shiri, T. Barszcz, R. Zimroz, A. Wyłomańska: Prediction of machine state for non-Gaussian degradation model using Hidden Markov Model approach, Eksploatacja i Niezawodnosc – Maintenance and Reliability 2025: 27(2), 2025
    3. J. Witulska, A. Zaleska, N. Kremzer-Osiadacz, A. Wyłomańska, I. Jabłoński: Robust variance estimators in application to segmentation of measurement data distorted by impulsive and non-Gaussian noise, Measurement 239, 115472, 2025
    4. W. Żuławiński, A. Wyłomańska: Errors-in-variables-based methodology of estimation and testing for infinite-variance periodic autoregressive models with additive noise, 32nd European Signal Processing Conference (EUSIPCO), Lyon, France, pp. 1087-1091, 2024
    5. K. Skowronek, R. Zimroz, A. Wyłomańska: Testing for finite variance with applications to vibration signals from rotating machines, J. Math. Industry 14(19), 2024
    6. K. Skowronek, M. Arendarczyk, R. Zimroz, A. Wyłomańska: Modified Greenwood statistic and its application for statistical testing, Journal of Computational and Applied Mathematics 452, 116122, 2024
    7. W. Żuławiński, J. Antoni, R, Zimroz, A. Wyłomańska: Robust coherent and incoherent statistics for detection of hidden periodicity in models with non-Gaussian additive noise, EURASIP J. Adv. Signal Process. 71, 2024
    8. W. Żuławiński, J. Antoni, R. Zimroz, A. Wyłomańska: Applications of robust statistics for cyclostationarity detection in non-Gaussian signals for local damage detection in bearings, Mechanical Systems and Signal Processing 214, 111367, 2024
    9. A. Michalak, R. Zdunek, R. Zimroz, A. Wylomanska: Influence of alpha-stable noise on the effectiveness of non-negative matrix factorization – simulations and real data analysis, Electronics 13(5), 829, 2024
    10. M. Gabor, R. Zdunek, R. Zimroz, A. Wyłomańska: Bearing damage detection with orthogonal and non-negative low-rank feature extraction, IEEE Transactions on Industrial Informatics 20(2), 2944-2955, 2024
    11. M. Gabor, R. Zdunek, R. Zimroz, A. Wyłomańska: Non-negative matrix underapproximation as optimal frequency band selector, In: IECON 2023- 49th Annual Conference of the IEEE Industrial Electronics Society. [Danvers, MA]: IEEE, 1-6, 2023
    12. W. Żuławiński, A. Wyłomańska: Empirical study of periodic autoregressive models with additive noise - estimation and testing, Communications in Statistics - Simulation and Computation, 1-26, 2023, doi: 10.1080/03610918.2023.2286217
    13. D. Kuzio, R. Zimroz, A. Wyłomańska: Identification of fault frequency variation in the envelope spectrum in the vibration-based local damage detection in changing load/speed conditions, Measurement 218(15), 113148, 2023
    14. K. Skowronek, T. Barszcz, J. Antoni, R. Zimroz, A. Wyłomańska: Assessment of background noise properties in time and time-frequency domains in the context of vibration-based local damage detection in real environment, Mechanical Systems and Signal Processing 199(15), 110465, 2023
    15. M.Gabor, R. Zdunek, R. Zimroz, J. Wodecki, A. Wyłomańska: Non-negative tensor factorization for vibration-based local damage detection, Mechanical Systems and Signal Processing 198, 110430, 2023
    16. W. Żuławiński, R. Zimroz, A. Wyłomańska: Yule-Walker-Based Approaches for Estimation of Noise-Corrupted Periodic Autoregressive Model - Finite- and Infinite-Variance Cases, 31st European Signal Processing Conference (EUSIPCO), Helsinki, Finland, pp. 1978-1982, 2023
    17. W. Żuławiński, A. Grzesiek, R. Zimroz, A. Wyłomańska: Identification and validation of periodic autoregressive model with additive noise: finite-variance case, Journal of Computational and Applied Mathematics 427, 115131, 2023
    18. P. Giri, A. Grzesiek, W. Żuławiński, S. Sundar, A. Wyłomańska: The modified Yule-Walker method for multidimensional infinite-variance periodic autoregressive model of order 1, Journal of the Korean Statistical Society, 2022

A UNIVERSAL DIAGNOSTIC AND PROGNOSTIC MODULE FOR CONDITION MONITORING SYSTEMS
OF COMPLEX MECHANICAL STRUCTURES OPERATING IN THE PRESENCE OF NON-GAUSSIAN DISTURBANCES AND VARIABLE OPERATING CONDITIONS

    Grant no.: OIR.01.01.01-00-0350/21 (Szybka Ścieżka)

    Funding agency: National Centre for Research and Development (NCBiR), Poland

    Funding period: 1.10.2021-31.12.2023

    Partners: Faculty of Pure and Applied Mathematics (WMat) WUST, Faculty of Geoengineering, Mining and Geology (WGGG) WUST, AMC Tech

    Budget for WUST: 1 926 000 PLN (c.a. 421 500 Euro)

    A key personnel consists of: prof. Agnieszka Wyłomańska (WMat), prof. Tomasz Barszcz (AMC Tech), prof. Radoslaw Zimroz (WGGG/KG/DMC).

    See the web page of the project

ANOMALOUS DIFFUSION PROCESSES
AND THEIR APPLICATION TO REAL DATA MODELLING

    Grant no.: 2016/21/B/ST1/00929 (OPUS)

    Funding agency: National Science Centre (NCN), Poland

    Funding period: 27.01.2017-26.01.2020

    Budget: 485 000 PLN

    Research team

    1. Agnieszka Wyłomańska (leader of the project, principal investigator)
    2. Janusz Gajda (investigator)
    3. Aleksandra Grzesiek (Ph.D. student)
    4. Piotr Kruczek (Ph.D. student)
    5. Rafał Połoczański (Ph.D. student)
    6. Katarzyna Maraj (student)
    7. Wojciech Żuławiński (student)
    8. Aleksei Chechkin (international collaborator, Potsdam University, Germany)
    9. Arun Kumar (international collaborator, IIT Ropar, India)
    10. Diego Krapf (international collaborator, Colorado State University, USA)
    11. S. Sundar (international collaborator, IIT Madras, India)
    12. Samudrajit Thapa (international collaborator, Potsdam University, Germany)
    13. Prashant Giri (international collaborator, IIT Madras, India)
    14. Anna Panorska (international collaborator, University of Nevada, USA)
    15. Tomasz Kozubowski (international collaborator, University of Nevada, USA)
    16. Holger Kantz (international collaborator, Max Planck Institute, Dresden, Germany)
    17. Marc Hoell (international collaborator, Max Planck Institute, Dresden, Germany)
    18. Denis Grebenkov (international collaborator, Ecole Polytechnique, France)
    19. Yann Lanoiselee (international collaborator, Ecole Polytechnique, France)

    Key words: anomalous difussion, subordinated process, stochastic modeling, statistical identification

    Tasks

    1. Analysis of subordinated processes with stationary increments
    2. Analysis of subordinated processes with inverse subordinators
    3. Analysis of long memory processes

    Selected publications

    1. A. Grzesiek, M. Teuerle, G. Sikora, A. Wyłomańska: Spatio-temporal dependence measures for alpha-stable bivariate AR(1) models , Journal of Time Series Analysis 2020, https://doi.org/10.1111/jtsa.12517
    2. A. Grzesiek, M. Teuerle, A. Wyłomańska:Cross-codifference for bidimensional VAR(1) time series with infinite variance, Communications in Statistics - Simulation and Computation 2020, https://doi.org/10.1080/03610918.2019.1670840
    3. A. Grzesiek, A. Wyłomańska: Subordinated Processes with Infinite Variance, In: Chaari F., Leskow J., Zimroz R., Wyłomańska A., Dudek A. (eds) Cyclostationarity: Theory and Methods – IV. CSTA 2017. Applied Condition Monitoring, vol 16, 111-135, Springer, Cham, 2020
    4. P. Poczynek, P. Kruczek, A. Wyłomańska: Ornstein-Uhlenbeck Process Delayed by Gamma Subordinator , In: Chaari F., Leskow J., Zimroz R., Wyłomańska A., Dudek A. (eds) Cyclostationarity: Theory and Methods – IV. CSTA 2017. Applied Condition Monitoring, vol 16, 147-165, Springer, Cham, 2020
    5. P. Kruczek, W. Żuławiński, P. Pagacz, A. Wyłomańska: Fractional lower order covariance based-estimator for Ornstein-Uhlenbeck process with stable distribution, Mathematica Applicanda 47, 259-292, 2019
    6. M. Szmigiel, A. Grzesiek, A. Wyłomańska, H. Kasprzak: Stable distribution in application to fixational eye movement description, Optica Applicata 49 (2), 365-377, 2019
    7. A. Kumar, A. Maheshwari, A. Wyłomańska: Linnik Levy Process and Its Generalization , Physica A 529, 121539, 2019
    8. G. Sikora, Ł. Bielak, A. Michalak, P. Miśta, A. Wyłomańska: Stochastic modelling of currency exchange rates with novel validation techniques, Physica A 523, 1202-1215, 2019
    9. A. Kumar, A. Wyłomańska, R. Połoczański, J. Gajda: Fractional Brownian motion delayed by tempered and inverse tempered stable subordinators, Methodology and Computing in Applied Probability 21(1), 185-202, 2019
    10. A. Grzesiek, S. Sundar, A. Wyłomańska: Fractional lower order covariance-based estimator for bidimensional AR(1) model with stable distribution, International Journal of Advances in Engineering Sciences and Applied Mathematics 11(3), 217-229, 2019
    11. J. Gajda Janusz, A. Wyłomańska, A. Kumar: Fractional Levy stable motion time-changed by gamma subordinator, Communications in Statistics - Theory and Methods 48, (24), 5953–5968, 2019
    12. A. Kumar, N. S. Upadhye, A. Wyłomańska, J. Gajda: Tempered Mittag-Leffler Levy Process, Communications in Statistics - Theory and Methods 48 (2), 396–411, 2019
    13. Y. Lanoiselee, D.S. Grebenkov, G. Sikora, A. Grzesiek, A. Wylomanska: Optimal parameters for anomalous diffusion exponent estimation from noisy data , Phys. Rev. E 98, 062139, 2018
    14. J. Gajda, A. Wyłomańska, H. Kantz, A. Chechkin, G. Sikora:Large deviations of time-averaged statistics for Gaussian processes , Statistics and Probability Letters 143, 47-55, 2018
    15. G. Sikora, A. Wyłomańska, D. Krapf:Recurrence statistics for anomalous diffusion regime change detection , Computational Statistics & Data Analysis 128, 380-394, 2018
    16. P. Kruczek, M. Polak, A. Wyłomańska, W. Kawalec, R. Zimroz: Application of compound Poisson process for modelling of ore flow in a belt conveyor system with cyclic loading,Journal International Journal of Mining, Reclamation and Environment 32(6), 376-391, 2018
    17. A. Grzesiek, J. Gajda, A. Wyłomańska, S. Sundar: Discriminating between scaled and fractional Brownian motion via p-variation statistics, International Journal of Advances in Engineering Sciences and Applied Mathematics 10(1), 9-14, 2018
    18. D. Kucharczyk, A. Wyłomańska, G. Sikora: Variance change point detection for fractional Brownian motion based on the likelihood ratio test, Physica A 490, 439-450, 2018
    19. G. Sikora, A. Wyłomańska, J. Gajda, L. Sole, E. J. Akin, M. M. Tamkun, D. Krapf: Elucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis, Phys. Rev. E 96, 062404, 2017
    20. G. Sikora, M. Teuerle, A. Wyłomańska, D. Grebenkov: Statistical properties of the anomalous scaling exponent estimator based on time averaged mean square displacement, Phys. Rev. E 96, 022132, 2017
    21. A. Kumar, A. Wyłomańska, J. Gajda: Stable Levy motion with inverse Gaussian subordinator, Physica A 482, 486–500, 2017
    22. G. Sikora, K. Burnecki, A. Wyłomańska: Mean-squared displacement statistical test for fractional Brownian motion, Phys. Rev. E 95, 032110, 2017
    23. A. Kumar, A. Wyłomańska, J. Gajda: Generalized fractional Laplace motion, Statistics and Probability Letters 124, 101-109, 2017
    24. M. Jabłońska, M. Teuerle, A. Wyłomańska: Bivariate sub-Gaussian model for stock indices returns, Physica A 486(15), 628–637, 2017