IDEAS home Printed from https://ideas.repec.org/p/lec/leecon/15-08.html
   My bibliography  Save this paper

Choosing the Right Skew Normal Distribution: the Macroeconomist’ Dilemma

Author

Listed:
  • Wojciech Charemza
  • Carlos Díaz
  • Svetlana Makarova

Abstract

The paper discusses the consequences of possible misspecification in fitting skew normal distributions to empirical data. It is shown, through numerical experiments, that it is easy to choose a distribution which is different from that which generated the sample, if the minimum distance criterion is used. The distributions compared are the two-piece normal, weighted skew normal and the generalized Balakrishnan skew normal distribution which covers a variety of other skew normal distributions, including the Azzalini distribution. The estimation method applied is the simulated minimum distance estimation with the Hellinger distance. It is suggested that, in case of similarity in values of distance measures obtained for different distributions, the choice should be made on the grounds of parameters’ interpretation rather than the goodness of fit. For monetary policy analysis, this suggests application of the weighted skew normal distribution, which parameters are directly interpretable as signals and outcomes of monetary decisions. This is supported by empirical evidence of fitting different skew normal distributions to the ex-post monthly inflation forecast errors for Poland, Russia, Ukraine and U.S.A., where estimations do not allow for clear distinction between the fitted distributions for Poland and U.S.A.

Suggested Citation

  • Wojciech Charemza & Carlos Díaz & Svetlana Makarova, 2015. "Choosing the Right Skew Normal Distribution: the Macroeconomist’ Dilemma," Discussion Papers in Economics 15/08, Division of Economics, School of Business, University of Leicester.
    • Handle: RePEc:lec:leecon:15/08
    as

    Download full text from publisher

    File URL: https://www.le.ac.uk/economics/research/RePEc/lec/leecon/dp15-08.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Andrade, Philippe & Le Bihan, Hervé, 2013. "Inattentive professional forecasters," Journal of Monetary Economics, Elsevier, vol. 60(8), pages 967-982.
    2. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    3. Marco Corazza & Florence Legros & Cira Perna & Marilena Sibillo, 2017. "Mathematical and Statistical Methods for Actuarial Sciences and Finance," Post-Print hal-01776135, HAL.
    4. Taylor, A M Robert, 2003. "Robust Stationarity Tests in Seasonal Time Series Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(1), pages 156-163, January.
    5. John W. Galbraith & Simon van Norden, 2012. "Assessing gross domestic product and inflation probability forecasts derived from Bank of England fan charts," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 175(3), pages 713-727, July.
    6. Luca Greco, 2011. "Minimum Hellinger distance based inference for scalar skew-normal and skew-t distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 120-137, May.
    7. Wojciech Charemza & Carlos Diaz Vela & Svetlana Makarova, 2013. "Inflation fan charts, monetary policy and skew normal distribution," Discussion Papers in Economics 13/06, Division of Economics, School of Business, University of Leicester.
    8. Michael P. Clements, 2004. "Evaluating the Bank of England Density Forecasts of Inflation," Economic Journal, Royal Economic Society, vol. 114(498), pages 844-866, October.
    9. Rossi, Barbara & Sekhposyan, Tatevik, 2019. "Alternative tests for correct specification of conditional predictive densities," Journal of Econometrics, Elsevier, vol. 208(2), pages 638-657.
    10. Michael P. Clements, 2014. "Forecast Uncertainty- Ex Ante and Ex Post : U.S. Inflation and Output Growth," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 206-216, April.
    11. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    12. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    13. M. Sharafi & J. Behboodian, 2008. "The Balakrishnan skew–normal density," Statistical Papers, Springer, vol. 49(4), pages 769-778, October.
    14. Balázs Égert & Ronald MacDonald, 2009. "Monetary Transmission Mechanism In Central And Eastern Europe: Surveying The Surveyable," Journal of Economic Surveys, Wiley Blackwell, vol. 23(2), pages 277-327, April.
    15. Anna Clara Monti, 2003. "A note on the estimation of the skew normal and the skew exponential power distributions," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 205-219.
    16. Martin Eling & Nicola Loperfido, 2020. "New mathematical and statistical methods for actuarial science and finance," The European Journal of Finance, Taylor & Francis Journals, vol. 26(2-3), pages 96-99, February.
    17. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    18. Carlos Bowles & Roberta Friz & Veronique Genre & Geoff Kenny & Aidan Meyler & Tuomas Rautanen, 2007. "The ECB survey of professional forecasters (SPF) – A review after eight years’ experience," Occasional Paper Series 59, European Central Bank.
    19. Arthur Pewsey, 2000. "Problems of inference for Azzalini's skewnormal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(7), pages 859-870.
    20. Kenneth F. Wallis, 2004. "An Assessment of Bank of England and National Institute Inflation Forecast Uncertainties," National Institute Economic Review, National Institute of Economic and Social Research, vol. 189(1), pages 64-71, July.
    21. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
    22. P. Hasanalipour & M. Sharafi, 2012. "A new generalized Balakrishnan skew-normal distribution," Statistical Papers, Springer, vol. 53(1), pages 219-228, February.
    23. Kajal Lahiri & Xuguang Sheng, 2010. "Measuring forecast uncertainty by disagreement: The missing link," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 514-538.
    24. Halina Kowalczyk, 2013. "Inflation fan charts and different dimensions of uncertainty. What if macroeconomic uncertainty is high?," NBP Working Papers 157, Narodowy Bank Polski.
    25. Víctor Gómez & Agustín Maravall, 1998. "Automatic Modeling Methods for Univariate Series," Working Papers 9808, Banco de España.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. A. Nanthakumar, 2020. "A Comparison of Archimedean Copula Models for approximating Bivariate Skew-Normal Distribution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 9(1), pages 1-70, January.
    2. Lee, Seohyun, 2017. "Three essays on uncertainty: real and financial effects of uncertainty shocks," MPRA Paper 83617, University Library of Munich, Germany.
    3. Ralph Vince, 2023. "Expectation and Optimal Allocations in Existential Contests of Finite, Heavy-Tail-Distributed Outcomes," Mathematics, MDPI, vol. 12(1), pages 1-25, December.
    4. Christophe Ley, 2014. "Flexible Modelling in Statistics: Past, present and Future," Working Papers ECARES ECARES 2014-42, ULB -- Universite Libre de Bruxelles.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wojciech Charemza & Carlos Diaz Vela & Svetlana Makarova, 2013. "Inflation fan charts, monetary policy and skew normal distribution," Discussion Papers in Economics 13/06, Division of Economics, School of Business, University of Leicester.
    2. Wojciech CHAREMZA & Carlos DÍAZ & Svetlana MAKAROVA, 2019. "Conditional Term Structure of Inflation Forecast Uncertainty: The Copula Approach," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 5-18, March.
    3. Barbara Rossi, 2019. "Forecasting in the presence of instabilities: How do we know whether models predict well and how to improve them," Economics Working Papers 1711, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2021.
    4. Charemza, Wojciech & Díaz, Carlos & Makarova, Svetlana, 2019. "Quasi ex-ante inflation forecast uncertainty," International Journal of Forecasting, Elsevier, vol. 35(3), pages 994-1007.
    5. Clements, Michael P., 2018. "Are macroeconomic density forecasts informative?," International Journal of Forecasting, Elsevier, vol. 34(2), pages 181-198.
    6. Rossi, Barbara & Ganics, Gergely & Sekhposyan, Tatevik, 2020. "From Fixed-event to Fixed-horizon Density Forecasts: Obtaining Measures of Multi-horizon Uncertainty from Survey Density Foreca," CEPR Discussion Papers 14267, C.E.P.R. Discussion Papers.
    7. Gergely Ganics & Barbara Rossi & Tatevik Sekhposyan, 2019. "From fixed-event to fixed-horizon density forecasts: Obtaining measures of multi-horizon uncertainty from survey density forecasts," Economics Working Papers 1689, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Lee, Seohyun, 2017. "Three essays on uncertainty: real and financial effects of uncertainty shocks," MPRA Paper 83617, University Library of Munich, Germany.
    9. Galvao, Ana Beatriz & Mitchell, James, 2019. "Measuring Data Uncertainty : An Application using the Bank of England’s “Fan Charts” for Historical GDP Growth," EMF Research Papers 24, Economic Modelling and Forecasting Group.
    10. Anne Sofie Jore & James Mitchell & Shaun P. Vahey, 2010. "Combining forecast densities from VARs with uncertain instabilities," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 621-634.
    11. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    12. Christian Kascha & Francesco Ravazzolo, 2010. "Combining inflation density forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(1-2), pages 231-250.
    13. Svetlana Makarova, 2018. "European Central Bank Footprints On Inflation Forecast Uncertainty," Economic Inquiry, Western Economic Association International, vol. 56(1), pages 637-652, January.
    14. Cees Diks & Valentyn Panchenko & Dick van Dijk, 2008. "Partial Likelihood-Based Scoring Rules for Evaluating Density Forecasts in Tails," Tinbergen Institute Discussion Papers 08-050/4, Tinbergen Institute.
    15. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Journal of Econometrics, Elsevier, vol. 163(2), pages 215-230, August.
    16. Krüger, Fabian & Nolte, Ingmar, 2016. "Disagreement versus uncertainty: Evidence from distribution forecasts," Journal of Banking & Finance, Elsevier, vol. 72(S), pages 172-186.
    17. Marcus P. A. Cobb, 2020. "Aggregate density forecasting from disaggregate components using Bayesian VARs," Empirical Economics, Springer, vol. 58(1), pages 287-312, January.
    18. Malte Knüppel, 2015. "Evaluating the Calibration of Multi-Step-Ahead Density Forecasts Using Raw Moments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 270-281, April.
    19. Rodríguez, Gabriel, 2017. "Modeling Latin-American stock and Forex markets volatility: Empirical application of a model with random level shifts and genuine long memory," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 393-420.
    20. Svetlana Makarova, 2016. "ECB footprints on inflation forecast uncertainty," Bank of Estonia Working Papers wp2016-5, Bank of Estonia, revised 19 Jul 2016.

    More about this item

    Keywords

    Skew Normal Distributions; Ex-post Uncertainty; Inflation Forecasting; Economic Policy;
    All these keywords.

    JEL classification:

    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:lec:leecon:15/08. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Abbie Sleath (email available below). General contact details of provider: https://edirc.repec.org/data/deleiuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.