IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

A Survey of Recent Theoretical Results for Time Series Models with GARCH Errors

  • W. K. Li
  • Shiqing Ling
  • Michael McAleer

This paper provides a review of some recent theoretical results for time series models with GARCH errors, and is directed towards practitioners. Starting with the simple ARCH model and proceeding to the GARCH model, some results for stationary and nonstationary ARMA-GARCH are summarized. Various new ARCH-type models, including double threshold ARCH and GARCH, ARFIMA-GARCH, CHARMA and vector ARMA-GARCH, are also reviewed.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.iser.osaka-u.ac.jp/library/dp/2001/dp0545.pdf
Download Restriction: no

Paper provided by Institute of Social and Economic Research, Osaka University in its series ISER Discussion Paper with number 0545.

as
in new window

Length:
Date of creation: Jun 2001
Date of revision:
Handle: RePEc:dpr:wpaper:0545
Contact details of provider: Postal: 6-1 Mihogaoka, Ibaraki, Osaka 567-0047
Fax: 81-6-6879-8583
Web page: http://www.iser.osaka-u.ac.jp/index-e.html
Email:


More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. van Dijk, Dick & Teräsvirta, Timo & Franses, Philip Hans, 2000. "Smooth Transition Autoregressive Models - A Survey of Recent Developments," SSE/EFI Working Paper Series in Economics and Finance 380, Stockholm School of Economics, revised 17 Jan 2001.
  2. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October.
  3. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
  4. Jeganathan, P., 1997. "On Asymptotic Inference in Linear Cointegrated Time Series Systems," Econometric Theory, Cambridge University Press, vol. 13(05), pages 692-745, October.
  5. Drost, F.C. & Nijman, T.E., 1992. "Temporal Aggregation of Garch Processes," Papers 9240, Tilburg - Center for Economic Research.
  6. Shiqing Ling & Michael McAleer, 2001. "On Adaptive Estimation in Nonstationary ARMA Models with GARCH Errors," ISER Discussion Paper 0548, Institute of Social and Economic Research, Osaka University.
  7. Lee, Sang-Won & Hansen, Bruce E., 1994. "Asymptotic Theory for the Garch(1,1) Quasi-Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 10(01), pages 29-52, March.
  8. Brooks, Chris, 2001. "A Double-Threshold GARCH Model for the French Franc/Deutschmark Exchange Rate," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 135-43, March.
  9. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
  10. Jan Beran & Yuanhua Feng, 1999. "Local Polynomial Estimation with a FARIMA-GARCH Error Process," CoFE Discussion Paper 99-08, Center of Finance and Econometrics, University of Konstanz.
  11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  12. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
  13. Drost, F.C. & Klaassen, C.A.J., 1997. "Efficient estimation in semiparametric GARCH models," Other publications TiSEM c7de3f1c-c456-433e-a1c6-2, Tilburg University, School of Economics and Management.
  14. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
  15. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  16. Shiqing Ling & W. K. Li & Michael McAleer, 2003. "Estimation and Testing for Unit Root Processes with GARCH (1, 1) Errors: Theory and Monte Carlo Evidence," CIRJE F-Series CIRJE-F-207, CIRJE, Faculty of Economics, University of Tokyo.
  17. Phillips, P C B & Durlauf, S N, 1986. "Multiple Time Series Regression with Integrated Processes," Review of Economic Studies, Wiley Blackwell, vol. 53(4), pages 473-95, August.
  18. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
  19. Drost, F.C. & Nijman, T.E., 1993. "Temporal aggregation of GARCH processes," Other publications TiSEM 0642fb61-c7f4-4281-b484-4, Tilburg University, School of Economics and Management.
  20. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
  21. Pesaran, H.M. & Potter, S.M., 1995. "A Floor and Ceiling Model of U.S. Output," Cambridge Working Papers in Economics 9407, Faculty of Economics, University of Cambridge.
  22. Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(01), pages 107-131, April.
  23. Seo, Byeongseon, 1999. "Distribution theory for unit root tests with conditional heteroskedasticity1," Journal of Econometrics, Elsevier, vol. 91(1), pages 113-144, July.
  24. Christian Francq & Jean-Michel Zakoïan, 1997. "Estimating Weak Garch Representations," Working Papers 97-40, Centre de Recherche en Economie et Statistique.
  25. Jiang, Jiancheng & Zhao, Quanshui & Hui, Yer Van, 2001. "Robust Modelling of ARCH Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 111-33, March.
  26. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
  27. Bera, Anil K & Higgins, Matthew L, 1993. " ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-66, December.
  28. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  29. Mak, T. K. & Wong, H. & Li, W. K., 1997. "Estimation of nonlinear time series with conditional heteroscedastic variances by iteratively weighted least squares," Computational Statistics & Data Analysis, Elsevier, vol. 24(2), pages 169-178, April.
  30. Drost, Feike C. & Klaassen, Chris A. J., 1997. "Efficient estimation in semiparametric GARCH models," Journal of Econometrics, Elsevier, vol. 81(1), pages 193-221, November.
  31. Lee, Tom K Y & Tse, Y K, 1991. "Term Structure of Interest Rates in the Singapore Asian Dollar Market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 6(2), pages 143-52, April-Jun.
  32. Herce, Miguel A., 1996. "Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors," Econometric Theory, Cambridge University Press, vol. 12(01), pages 129-153, March.
  33. Shiqing Ling & Michael McAleer, 2001. "Stationarity and the Existence of Moments of a Family of GARCH Processes," ISER Discussion Paper 0535, Institute of Social and Economic Research, Osaka University.
  34. Lumsdaine, Robin L, 1996. "Consistency and Asymptotic Normality of the Quasi-maximum Likelihood Estimator in IGARCH(1,1) and Covariance Stationary GARCH(1,1) Models," Econometrica, Econometric Society, vol. 64(3), pages 575-96, May.
  35. Davis, Richard & Resnick, Sidney, 1985. "More limit theory for the sample correlation function of moving averages," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 257-279, September.
  36. Fornari, Fabio & Mele, Antonio, 1997. "Sign- and Volatility-Switching ARCH Models: Theory and Applications to International Stock Markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(1), pages 49-65, Jan.-Feb..
  37. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(02), pages 280-310, April.
  38. Kim, Kiwhan & Schmidt, Peter, 1993. "Unit root tests with conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 59(3), pages 287-300, October.
  39. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  40. He, Changli & Ter svirta, Timo, 1999. "FOURTH MOMENT STRUCTURE OF THE GARCH(p,q) PROCESS," Econometric Theory, Cambridge University Press, vol. 15(06), pages 824-846, December.
  41. Leybourne, S J & McCabe, B P M & Tremayne, A R, 1996. "Can Economic Time Series Be Differenced to Stationarity?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 435-46, October.
  42. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
  43. He, Changli & Terasvirta, Timo, 1999. "Properties of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 92(1), pages 173-192, September.
  44. 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.
  45. Robinson, P M, 1988. "Semiparametric Econometrics: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(1), pages 35-51, January.
  46. Horv th, Lajos & Kokoszka, Piotr, 2001. "LARGE SAMPLE DISTRIBUTION OF WEIGHTED SUMS OF ARCH(p) SQUARED RESIDUAL CORRELATIONS," Econometric Theory, Cambridge University Press, vol. 17(02), pages 283-295, April.
  47. Linton, Oliver, 1993. "Adaptive Estimation in ARCH Models," Econometric Theory, Cambridge University Press, vol. 9(04), pages 539-569, August.
  48. Karanasos, Menelaos, 1999. "The second moment and the autocovariance function of the squared errors of the GARCH model," Journal of Econometrics, Elsevier, vol. 90(1), pages 63-76, May.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:dpr:wpaper:0545. 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: (Fumiko Matsumoto)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.