Dr hab. Second Bwanakare, prof. WSIiZ

Profesor w Katedrze Ekonomii i Finansów.

Zatrudniony w Wyższej Szkole Informatyki i Zarządzania od 2006 roku.

Doktor habilitowany w zakresie nauk społecznych (Uniwersytet Łódzki, Wydział Socjologiczno-Ekonomiczny, 2020), doktor ekonomii (Uniwersytet Warszawski, Wydział Ekonomii, 1995), magister ekonomii (SGPIS, Wydział Cybernetyki Ekonomicznej i Informatyki, 1990).

Jego zainteresowania naukowe koncentrują się na: modelowaniu kompleksowych (nieliniowych) systemów. Głównym narzędziem tego modelowania jest niedawno zaproponowane podejście statystyczno-ekonometryczne, zwane „ekonometrią nie ekstensywnej entropii” opartej na entropii Tsallis (rozkład prawa potęgowego), statystycznej teorii informacji i klasycznej ekonometrii opisującej zjawiska ergodyczne (rozkład normalny).

Jest autorem wielu artykułów i książek opublikowanych w czasopismach międzynarodowych w zakresie modelowania nieliniowych zjawisk statystyczno-ekonomicznych w warunkach problemów odwrotnych.

Od 2013 roku międzynarodowy ekspert  w Państwowej Komisji Akredytacyjnej(PKA) w Warszawie, od 2016 roku konsultant w zakresie metodologii statystycznej w Rzeszowskim Urzędzie Statystycznym.


Prowadzone przedmioty:

Ekonometria, Wnioskowanie statystyczne, Ekonometria dynamiczna finansowa, Statystyka opisowa, Statystyka matematyczna, Makroekonomia, Prognozowanie i symulacji, Analiza matematyczna dla ekonomistów.

Materiały dla studentów dostępne są na platformie BlackBoard.



Dr hab. Second Bwanakare, prof. WSIiZ
Katedra Ekonomii i Finansów
e-mail: sbwanakare@wsiz.rzeszow.pl
35-225 Rzeszów, ul. Sucharskiego 2
p. RA 131




Master of Science : 1990, econometrics, statistics, and demography, SGIPS (Warsaw School of Economics), Ph.D. : 1995, University of Warsaw, Faculty of Economic Sciences, thesis title: “Growth-Oriented Structural Adjustment Policies for a Dual Economy. An Econometrical Assessment”.

Associate professor : 2020, University of Lodz, Poland

Habilitation degree research field : « Non-Extensive Entropy Econometrics for Low Frequency Series: National Accounts-Based Inverse Problems ». This proposed subdiscipline of econometrics generalizes the maximum entropy econometrics on nonlinear systems using Tsallis entropy and statistical information theory formalism.

CAREER (recent)

From 2016 :

Consultant – statistical analysis and methodology,

Polish Statistical Office

From 2013:

International expert at the Polish Accreditation Committee (minister of higher education), Warsaw.


The main goal of our scientific and research activity is reflected in the publications presented by us in recent years. Familiarization with the important concepts of nonadditive thermodynamic statistics has directed us interest to study non-ergodic (inverse-problems) phenomena characterized by greater complexity than those described in the attractor of the Lindenberg central theorem-limit, of which Shannon’s entropy and most traditional econometric models are limited to. In the centre of non-extensive statistics and entropy of Tsallis points out a PL distribution. After learning about the properties of this entropy, about its more general character in comparison with Shannon’s entropy, we came to the conclusion that its connection with Kullback-Leibler-Jaynes statistical information formalism should provide an econometric modelling tool potentially capable of more general analysis of systems including non-ergodic ones, examples of which are fractal and multifractal phenomena. These premises have conditioned the main scientific goal of our research over the past years.

Thus, the rationale of proposing the methodology of non-extensive (cross-) entropy econometrics (NCEE) remains the fact that in the real world, socioeconomic rare events may have higher impact than more frequent events could when seen with respect to Gaussian distribution. As alluded to in our recent publications, long-range correlation and observed time invariant scale structure of high frequency series may still be conserved—in some classes of nonlinear models—through a process of time (or space) aggregation of statistical data. Our research shows that such a process is better described by a power-law (PL)-related model belonging to Tsallis non-additive statistics. The methodology extends PL to the Kullback-Leibler-Jaynes statistical theory of information. Next, this formalism allows for connecting to the system an econometric model in the Bayesian context. In this context, an ad hoc new statistical inference, different from the Neyman classical one based on the Lindeberg central theorem-limit, has been proposed to allow for real world implementation of the methodology. Because of this and based on existing literature, the approach is termed Non-extensive (Cross-) Entropy Econometrics or using a less technical expression, Superstar-Generalized Econometrics, to emphasize the role in a society( or elsewhere) of “superstars” (sparse or rare events, e.g., high earnings in financial markets, the economic consequences of a hurricane, earnings of artists or CEOs of large firms with respect to exceptional popularity, etc..). Traditional econometrics generally considers that outlier data should be excluded from the original data before any econometric modelling.

Our current research activity extends the recently proposed model to simultaneous equation models, based on the presumption in real life of interconnected non-linear phenomena, at different levels of complexity.



Bwanakare, (et al.), Reconciling conflicting cross-border data sources for updating national accounts: The cross-entropy econometrics approach, Statistical Journal of the IAOS, , pp. 1-9, 2020, doi: 10.3233/SJI-180489

Bwanakare, Non-Extensive Entropy Econometrics for Low Frequency Series: National Accounts-Based Inverse Problems, published by De Gruyter Open Ltd, Warsaw/Berlin, part of Walter de Gruyter GmbH, Berlin/Boston, monograph, July 2019. https://www.degruyter.com/view/title/539862?rskey=5Bcqpt&result=1

Bwanakare, Non-Extensive Entropy Econometrics and CES production Models: Country Case Study, Journal of International Association of Official Statistics (IAOS), 2016. https://content.iospress.com/articles/statistical-journal-of-the-iaos/sji1021

Bwanakare, (et al.) Predicting Gross Domestic Product Components through Tsallis Entropy Econometrics, Polish Academy of Sciences, Acta Physica Polonica A, Vol. 129/5, Mai 2016, http://przyrbwn.icm.edu.pl/APP/PDF/129/a129z5p18.pdf

Bwanakare, (et al.) Quantitative Characteristics of Correlations of Meteorological Data, Polish Academy of Sciences, Acta Physica Polonica A, Vol. 129/5, Mai 2016, DOI: 10.12693/APhysPolA.129.922.

Bwanakare, Greenhouse Emission Forecast as an Inverse Stochastic Problem: A Cross-Entropy Econometrics Approach. Polish Academy of Sciences, Acta Physica Polonica A 2015, 127/3A, March 2015, http://przyrbwn.icm.edu.pl/APP/PDF/127/a127z3ap02.pdf

Bwanakare, Non-Extensive Entropy Econometrics: New Statistical Features of Constant Elasticity of Substitution-Related Models. Entropy 2014, 16, 2713-2728, http://www.mdpi.com/1099-4300/16/5/2713

Bwanakare, Balancing an Ill-Behaved National Accounts Table Under PL Property Hypothesis, Polish Academy of Sciences, Statistical Review, No. 3/9 2014

Bwanakare, A Stochastic Non-Homogeneous Constant Elasticity of Substitution Problem: A Non-Extensive Entropy Estimation Approach, Polish Academy of Sciences, Acta Physica Polonica A, vol 123/3, March 2013, DOI: 10.12693 /APhysPolA.123.502 or http://przyrbwn.icm.edu.pl/APP/PDF/123/a123z3p02.pdf

Bwanakare, Non-Extensive Entropy Econometric Model (NEE): The Case of Labour Demand in the Subcarpate Province, Polish Academy of Sciences, Acta Physica Polonica A, April 2010, vol.117 / 4, http://przyrbwn.icm.edu.pl/APP/PDF/117/a117z457.pdf

Conducted courses:

Econometrics, Info-metrics, Macroeconomics, Descriptive statistics, Probability and Inferential statistics, Dynamical financial econometrics, National accounting, Graduate and under-graduate seminars, Research level seminars in quantitative economics.

Materials for students are available at the relevant courses at the Blackboard platform.


Contact data

Dr hab. prof. WSIZ Second Bwanakare
Katedra Ekonomii i Finansów
e-mail: sbwanakare@wsiz.rzeszow.pl
35-225 Rzeszów, ul. Sucharskiego 2
Pok. RA 131

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