IDEAS home Printed from
   My bibliography  Save this paper

Modelling the Density of Egyptian Quarterly CPI Inflation


  • Doaa Akl Ahmed

    (University of Benha)

  • Mamdouh M. Abdelsalam


This paper aims at modelling the density of quarterly inflation based on time-varying conditional variance, skewness and kurtosis model developed by Leon, Rubio, and Serna (2005). They model higher-order moments as GARCH-type processes by applying a Gram-Charlier series expansion of the normal density function. We estimated seven univariate models, including GARCH-M and TARCH-M models, assuming three different distributions for the error term, namely: normal, student t, and GED distributions. Additionally, the model that allows for non-constant higher order moments, GARCHSK-M, has been estimated. Moreover, the paper utilizes two multivariate models, Dynamic Conditional Correlation (DCC) and Diagonal VECH models to isolate the time-varying conditional correlations between inflation and two financial variables, including growth in domestic credit and real exchange rate. Results revealed the significant persistence in conditional variance, skewness and kurtosis, which indicate high asymmetry of inflation. Diagnostic tests indicated that models with invariant volatility, skewness and kurtosis are inferior to the models that permit them to vary over time. Moreover, depending on models of static historic correlation between inflation and the highly financial variables in order to evaluate inflation dynamic behavior is misleading and is a poor informative. Comparing the predictive power of different models showed that basic models are more accurate in forecasting out-of-sample inflation according to some criterions and GARCHSK-M is better for other criterions. By applying Diebold and Mariano’s (1995) encompassing test, it was found that all models could be combined together to form a more accurate forecast. We have done the combination of forecasts using equal weights, Bayesian Model Averaging (BMA), and Dynamic Model Averaging (DMA). Results of forecast combination showed that the combined forecasts outperform the projection of best single model.

Suggested Citation

  • Doaa Akl Ahmed & Mamdouh M. Abdelsalam, 2015. "Modelling the Density of Egyptian Quarterly CPI Inflation," Working Papers 936, Economic Research Forum, revised Aug 2015.
  • Handle: RePEc:erg:wpaper:936

    Download full text from publisher

    File URL:
    Download Restriction: no

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    2. Gary Koop & Dimitris Korobilis, 2012. "Forecasting Inflation Using Dynamic Model Averaging," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 867-886, August.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. 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.
    5. Armstrong, J. Scott, 1989. "Combining forecasts: The end of the beginning or the beginning of the end?," International Journal of Forecasting, Elsevier, vol. 5(4), pages 585-588.
    6. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    7. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    8. Doaa Akl Ahmed, 2011. "Modelling the Density of Inflation Using Autoregressive Conditional Heteroscedasticity, Skewness, and Kurtosis Models," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 1-28, November.
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    11. Engle, Robert F. (ed.), 1995. "ARCH: Selected Readings," OUP Catalogue, Oxford University Press, number 9780198774327.
    12. Laurence Ball & N. Gregory Mankiw, 1995. "Relative-Price Changes as Aggregate Supply Shocks," The Quarterly Journal of Economics, Oxford University Press, vol. 110(1), pages 161-193.
    13. Michael F. Bryan & Stephen G. Cecchetti, 1999. "Inflation And The Distribution Of Price Changes," The Review of Economics and Statistics, MIT Press, vol. 81(2), pages 188-196, May.
    14. Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(4), pages 465-487, December.
    15. Kurt Brannas & Niklas Nordman, 2003. "Conditional skewness modelling for stock returns," Applied Economics Letters, Taylor & Francis Journals, vol. 10(11), pages 725-728.
    16. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    17. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    18. Leon, Angel & Rubio, Gonzalo & Serna, Gregorio, 2005. "Autoregresive conditional volatility, skewness and kurtosis," The Quarterly Review of Economics and Finance, Elsevier, vol. 45(4-5), pages 599-618, September.
    19. Friedman, Milton, 1977. "Nobel Lecture: Inflation and Unemployment," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 451-472, June.
    20. Grier, Kevin B. & Perry, Mark J., 1996. "Inflation, inflation uncertainty, and relative price dispersion: Evidence from bivariate GARCH-M models," Journal of Monetary Economics, Elsevier, vol. 38(2), pages 391-405, October.
    Full references (including those not matched with items on IDEAS)

    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. repec:zbw:cfswop:wp200508 is not listed on IDEAS
    2. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    4. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    5. Halkos, George & Tzirivis, Apostolos, 2018. "Effective energy commodities’ risk management: Econometric modeling of price volatility," MPRA Paper 90781, University Library of Munich, Germany.
    6. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, April.
    7. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    8. Palandri, Alessandro, 2009. "Sequential conditional correlations: Inference and evaluation," Journal of Econometrics, Elsevier, vol. 153(2), pages 122-132, December.
    9. Yang (Greg) Hou & Mark Holmes, 2020. "Do higher order moments of return distribution provide better decisions in minimum-variance hedging? Evidence from US stock index futures," Australian Journal of Management, Australian School of Business, vol. 45(2), pages 240-265, May.
    10. Choi, Pilsun & Nam, Kiseok, 2008. "Asymmetric and leptokurtic distribution for heteroscedastic asset returns: The SU-normal distribution," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 41-63, January.
    11. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    12. Brian H. Boyer & Michael S. Gibson, 1997. "Evaluating forecasts of correlation using option pricing," International Finance Discussion Papers 600, Board of Governors of the Federal Reserve System (U.S.).
    13. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    14. Dark Jonathan Graeme, 2010. "Estimation of Time Varying Skewness and Kurtosis with an Application to Value at Risk," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(2), pages 1-50, March.
    15. Audrone Virbickaite & M. Concepción Ausín & Pedro Galeano, 2015. "Bayesian Inference Methods For Univariate And Multivariate Garch Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 76-96, February.
    16. King, Daniel & Botha, Ferdi, 2015. "Modelling stock return volatility dynamics in selected African markets," Economic Modelling, Elsevier, vol. 45(C), pages 50-73.
    17. repec:wyi:journl:002081 is not listed on IDEAS
    18. Chong, James, 2005. "The forecasting abilities of implied and econometric variance-covariance models across financial measures," Journal of Economics and Business, Elsevier, vol. 57(5), pages 463-490.
    19. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Hong, Yongmiao & Li, Haitao & Zhao, Feng, 2007. "Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates," Journal of Econometrics, Elsevier, vol. 141(2), pages 736-776, December.
    21. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    22. Wiper, Michael Peter & García de la Fuente, Cristina & Galeano San Miguel, Pedro, 2014. "Bayesian estimation of a dynamic conditional correlation model with multivariate Skew-Slash innovations," DES - Working Papers. Statistics and Econometrics. WS ws141711, Universidad Carlos III de Madrid. Departamento de Estadística.

    More about this item


    Access and download statistics


    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:erg:wpaper:936. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: .

    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: Sherine Ghoneim (email available below). General contact details of provider: .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.