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A prospective study of the k-factor Gegenbauer processes with heteroscedastic errors and an application to inflation rates

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Author Info

  • Dominique Guegan

    ()
    (IDHE - Institutions et Dynamiques Historiques de l'Economie - CNRS : UMR8533 - Université Panthéon-Sorbonne - Paris I - Université Paris VIII Vincennes-Saint Denis - Université de Paris X - Nanterre - École normale supérieure de Cachan - ENS Cachan)

Abstract

We investigate some statistical properties of the new k-factor Gegenbauer process with heteroscedastic noises One of the goals of the paper is to give tools which permit to use this model to explain the behaviour of certain data sets in finance and in macroeconomics. Monte Carlo experiments are provided to calibrate the theoretical properties. Applications on consumer price indexes and inflation rates are done;

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File URL: http://halshs.archives-ouvertes.fr/docs/00/20/13/14/PDF/guegan_finance-india.pdf
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Bibliographic Info

Paper provided by HAL in its series Post-Print with number halshs-00201314.

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Date of creation: 2003
Date of revision:
Publication status: Published, Finance India, 2003, XVII, 1, 165 - 197
Handle: RePEc:hal:journl:halshs-00201314

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Related research

Keywords: GIGARCH process – estimation theory – Inflation rates – prices indexes.;

References

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  1. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
  2. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
  3. Barsky, Robert B., 1987. "The Fisher hypothesis and the forecastability and persistence of inflation," Journal of Monetary Economics, Elsevier, vol. 19(1), pages 3-24, January.
  4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  5. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
  6. Drost, Feike C & Nijman, Theo E, 1993. "Temporal Aggregation of GARCH Processes," Econometrica, Econometric Society, vol. 61(4), pages 909-27, July.
  7. Liu, Ming, 1998. "Asymptotics Of Nonstationary Fractional Integrated Series," Econometric Theory, Cambridge University Press, vol. 14(05), pages 641-662, October.
  8. Hassler, Uwe & Wolters, Jurgen, 1995. "Long Memory in Inflation Rates: International Evidence," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(1), pages 37-45, January.
  9. John Y. Campbell & Robert J. Shiller, 2001. "Valuation Ratios and the Long-Run Stock Market Outlook: An Update," NBER Working Papers 8221, National Bureau of Economic Research, Inc.
  10. Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991. "Testing the Null Hypothesis of Stationarity Against the Alternative of a Unit Root: How Sure Are We That Economic Time Series Have a Unit Root?," Cowles Foundation Discussion Papers 979, Cowles Foundation for Research in Economics, Yale University.
  11. Chambers, Marcus J, 1998. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1053-72, November.
  12. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  13. Drost, Feike C. & Werker, Bas J. M., 1996. "Closing the GARCH gap: Continuous time GARCH modeling," Journal of Econometrics, Elsevier, vol. 74(1), pages 31-57, September.
  14. Rose, Andrew Kenan, 1988. " Is the Real Interest Rate Stable?," Journal of Finance, American Finance Association, vol. 43(5), pages 1095-1112, December.
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  16. Bougerol, Philippe & Picard, Nico, 1992. "Stationarity of Garch processes and of some nonnegative time series," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 115-127.
  17. Chung, Ching-Fan & Baillie, Richard T, 1993. "Small Sample Bias in Conditional Sum-of-Squares Estimators of Fractionally Integrated ARMA Models," Empirical Economics, Springer, vol. 18(4), pages 791-806.
  18. Franses, Philip Hans & Ooms, Marius, 1997. "A periodic long-memory model for quarterly UK inflation," International Journal of Forecasting, Elsevier, vol. 13(1), pages 117-126, March.
  19. Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
  20. Lobato, Ignacio N & Velasco, Carlos, 2000. "Long Memory in Stock-Market Trading Volume," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 410-27, October.
  21. D Marinucci & Peter M. Robinson, 1998. "Weak convergence of multivariate fractional processes," LSE Research Online Documents on Economics 2322, London School of Economics and Political Science, LSE Library.
  22. Smith, Jeremy & Yadav, Sanjay, 1994. "Forecasting costs incurred from unit differencing fractionally integrated processes," International Journal of Forecasting, Elsevier, vol. 10(4), pages 507-514, December.
  23. Ferrara, Laurent & Guegan, Dominique, 2001. "Forecasting with k-Factor Gegenbauer Processes: Theory and Applications," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(8), pages 581-601, December.
  24. Jan Beran & Dirk Ocker, 1999. "SEMIFAR Forecasts, with Applications to Foreign Exchange Rates," CoFE Discussion Paper 99-13, Center of Finance and Econometrics, University of Konstanz.
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Citations

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Cited by:
  1. repec:hal:cesptp:halshs-00375758 is not listed on IDEAS
  2. Abdou Kâ Diongue & Dominique Guegan, 2008. "Estimation of k-factor GIGARCH process : a Monte Carlo study," Documents de travail du Centre d'Economie de la Sorbonne b08004, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Ferrara, L. & Guégan, D., 2008. "Business surveys modelling with Seasonal-Cyclical Long Memory models," Working papers 224, Banque de France.
  4. repec:hal:cesptp:halshs-00188264 is not listed on IDEAS
  5. repec:ebl:ecbull:v:3:y:2008:i:29:p:1-10 is not listed on IDEAS
  6. repec:hal:cesptp:halshs-00307606 is not listed on IDEAS
  7. Diongue, Abdou Kâ & Guégan, Dominique, 2007. "The stationary seasonal hyperbolic asymmetric power ARCH model," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1158-1164, June.
  8. repec:hal:cesptp:halshs-00185370 is not listed on IDEAS
  9. repec:hal:cesptp:halshs-00179269 is not listed on IDEAS
  10. Dufrenot, Gilles & Guegan, Dominique & Peguin-Feissolle, Anne, 2005. "Modelling squared returns using a SETAR model with long-memory dynamics," Economics Letters, Elsevier, vol. 86(2), pages 237-243, February.
  11. Abdou Kâ Diongue & Dominique Guégan & Bertrand Vignal, 2007. "Forecasting electricity spot market prices with a k-factor GIGARCH process," Documents de travail du Centre d'Economie de la Sorbonne b07058, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Nov 2009.

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