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An Introduction to Hypergeometric Functions for Economists

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  • Abadir, Karim

Abstract

Hypergeometric functions are a generalization of exponential functions. They are explicit, computable functions that can also be manipulated analytically. The functions and series we use in quantitative economics are all special cases of them. In this paper, a unified approach to hypergeometic functions is given. As a result, some potentially useful general applications emerge such as in statistical distribution theory, applied econonometrics and economic theory. The greatest benefit from using these functions stems from the fact that they provide the parsimonious explicit (and interpretable) solutions to a wide range of general problems.

Suggested Citation

  • Abadir, Karim, 1995. "An Introduction to Hypergeometric Functions for Economists," Discussion Papers 9510, University of Exeter, Department of Economics.
  • Handle: RePEc:exe:wpaper:9510
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    References listed on IDEAS

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    1. Garcia, R. & Bonomo, M., 1993. "Disappointment Aversion as a Solution to the Equity Premium and the Risk- Free Rate Puzzles," Cahiers de recherche 9334, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Sutherland, Alan, 1997. "Fiscal crises and aggregate demand: can high public debt reverse the effects of fiscal policy?," Journal of Public Economics, Elsevier, vol. 65(2), pages 147-162, August.
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    Cited by:

    1. Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, vol. 140(2), pages 695-718, October.
    2. Jennifer Castle & David Hendry, 2010. "Automatic Selection for Non-linear Models," Economics Series Working Papers 473, University of Oxford, Department of Economics.
    3. A. Sancetta & Satchell, S.E., 2001. "Bernstein Approximations to the Copula Function and Portfolio Optimization," Cambridge Working Papers in Economics 0105, Faculty of Economics, University of Cambridge.
    4. Boucekkine, R. & Ruiz-Tamarit, J.R., 2008. "Special functions for the study of economic dynamics: The case of the Lucas-Uzawa model," Journal of Mathematical Economics, Elsevier, vol. 44(1), pages 33-54, January.
    5. Abadir, Karim M. & Caggiano, Giovanni & Talmain, Gabriel, 2013. "Nelson–Plosser revisited: The ACF approach," Journal of Econometrics, Elsevier, vol. 175(1), pages 22-34.
    6. Proietti, Tommaso & Lütkepohl, Helmut, 2013. "Does the Box–Cox transformation help in forecasting macroeconomic time series?," International Journal of Forecasting, Elsevier, vol. 29(1), pages 88-99.
    7. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.
    8. M. Karanasos & J. Kim, 2003. "Moments of the ARMA--EGARCH model," Econometrics Journal, Royal Economic Society, vol. 6(1), pages 146-166, June.
    9. Abadir, Karim M. & Talmain, Gabriel, 2005. "Autocovariance functions of series and of their transforms," Journal of Econometrics, Elsevier, vol. 124(2), pages 227-252, February.
    10. Giacomini, Raffaella & Haefke, Christian & White, Halbert & Gottschling, Andreas, 2002. "Hypernormal Densities," University of California at San Diego, Economics Working Paper Series qt9wr373nt, Department of Economics, UC San Diego.
    11. Abadir, Karim M. & Lawford, Steve, 2004. "Optimal asymmetric kernels," Economics Letters, Elsevier, vol. 83(1), pages 61-68, April.
    12. Lubrano, Michel & Ndoye, Abdoul Aziz Junior, 2016. "Income inequality decomposition using a finite mixture of log-normal distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 830-846.
    13. Menelaos Karanasos & J. Kim, "undated". "Alternative GARCH in Mean Models: An Application to the Korean Stock Market," Discussion Papers 00/25, Department of Economics, University of York.
    14. Karim M. Abadir & Adriana Cornea, 2012. "Approximating Moments by Nonlinear Transformations," Working Paper series 22_12, Rimini Centre for Economic Analysis.
    15. Abadir, Karim M. & Lucas, Andre, 2004. "A comparison of minimum MSE and maximum power for the nearly integrated non-Gaussian model," Journal of Econometrics, Elsevier, vol. 119(1), pages 45-71, March.
    16. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modelling Multivariate Interest Rates using Time-Varying Copulas and Reducible Non-Linear Stochastic Differential," Economics Working Papers 09-02, Queen's Management School, Queen's University Belfast.
    17. Castle, Jennifer L. & Hendry, David F., 2010. "A low-dimension portmanteau test for non-linearity," Journal of Econometrics, Elsevier, vol. 158(2), pages 231-245, October.
    18. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2009. "Modeling Multivariate Interest Rates using Time-Varying Copulas and Reducible Stochastic Differential Equations," Working Papers halshs-00408014, HAL.
    19. Mark Vancauteren & Daniel Weiserbs, 2011. "Intra-European Trade of Manufacturing Goods: An Extension of the Gravity Model," International Econometric Review (IER), Econometric Research Association, vol. 3(1), pages 1-24, April.
    20. Giacomini, Raffaella & Gottschling, Andreas & Haefke, Christian & White, Halbert, 2008. "Mixtures of t-distributions for finance and forecasting," Journal of Econometrics, Elsevier, vol. 144(1), pages 175-192, May.
    21. Ruijun Bu & Kaddour Hadri, 2005. "Estimating the Risk Neutral Probability Density Functions Natural Spline versus Hypergeometric Approach Using European Style Options," Research Papers 200510, University of Liverpool Management School.
    22. José Ramón Ruiz Tamarit & Manuel Sánchez Moreno, 2006. "Optimal Regulation And Growth In A Natural-Resource-Based Economy," Working Papers. Serie AD 2006-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).

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    Keywords

    MATHEMATICAL ECONOMICS;

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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