The Stationary Seasonal Hyperbolic Asymmetric Power ARCH model
Most financial time series exhibit seasonality, persistence (hyperbolic decay of the autocorrelation function), asymmetric behavior and leptokurtosis. In this paper, we introduce the stationary Seasonal Hyperbolic APARCH model, which can take into account the previous features. We then investigate the probabilistic properties of the process e.g the strict and weak stationarity of the process and the long memory property.
|Date of creation:||Jun 2007|
|Date of revision:|
|Publication status:||Published in Statistics and Probability Letters, Elsevier, 2007, 77 (11), pp.1158-1164. <10.1016/j.spl.2007.02.007>|
|Note:||View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00179275|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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.:
- Dominique Guegan, 2005.
"How can we Define the Concept of Long Memory? An Econometric Survey,"
Taylor & Francis Journals, vol. 24(2), pages 113-149.
- Dominique Guegan, 2005. "How can we define the concept of long memory ? An econometric survey," Post-Print halshs-00179343, HAL.
- Guégan D., 2004. "How Can We Define The Concept of Long Memory? An Econometric Survey," School of Economics and Finance Discussion Papers and Working Papers Series 178, School of Economics and Finance, Queensland University of Technology.
- Schwert, G.W., 1989.
"Stock Volatility And The Crash Of '87,"
89-01, Rochester, Business - General.
- Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
- Bollerslev, Tim & Ghysels, Eric, 1996.
"Periodic Autoregressive Conditional Heteroscedasticity,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 14(2), pages 139-51, April.
- Bollerslev, T. & Ghysels, E., 1994. "Periodic Autoregressive Conditional Heteroskedasticity," Cahiers de recherche 9408, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- Bollerslev, T. & Ghysels, E., 1994. "Periodic Autoregressive Conditional Heteroskedasticity," Cahiers de recherche 9408, Universite de Montreal, Departement de sciences economiques.
- Liu, Shi-Miin & Brorsen, B Wade, 1995. "Maximum Likelihood Estimation of a Garch-Stable Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(3), pages 273-85, July-Sept.
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
- Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
- Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
- Hwang, Y., 2001. "Asymmetric long memory GARCH in exchange return," Economics Letters, Elsevier, vol. 73(1), pages 1-5, October.
- Pagan, A.R. & Schwert, G.W., 1989.
"Alternative Models For Conditional Stock Volatility,"
89-02, Rochester, Business - General.
- Pagan, Adrian R. & Schwert, G. William, 1990. "Alternative models for conditional stock volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 267-290.
- Adrian R. Pagan & G. William Schwert, 1989. "Alternative Models For Conditional Stock Volatility," NBER Working Papers 2955, National Bureau of Economic Research, Inc.
- Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Y. K. Tse, 1998. "The conditional heteroscedasticity of the yen-dollar exchange rate," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 49-55.
- Bollerslev, Tim, 1986.
"Generalized autoregressive conditional heteroskedasticity,"
Journal of Econometrics,
Elsevier, vol. 31(3), pages 307-327, April.
- Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
- Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
- Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
- Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
- Ole E. Barndorff-Nielsen & Karsten Prause, 2001. "Apparent scaling," Finance and Stochastics, Springer, vol. 5(1), pages 103-113.
- Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
- Dominique Guegan, 2004. "How Can We Define the Long Memory Concept? An Econometric Survey," Econometric Society 2004 Australasian Meetings 361, Econometric Society.
- 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.
- Dominique Guegan, 2003. "A prospective study of the k-factor Gegenbauer processes with heteroscedastic errors and an application to inflation rates," Post-Print halshs-00201314, HAL.
- 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.
- Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665 National Bureau of Economic Research, Inc.
- Engle, Robert F. & White (the late), Halbert (ed.), 1999. "Cointegration, Causality, and Forecasting: Festschrift in Honour of Clive W. J. Granger," OUP Catalogue, Oxford University Press, number 9780198296836, May.
- 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.
- He, Changli & Teräsvirta, Timo, 1999. "Higher-order dependence in the general Power ARCH process and a special case," SSE/EFI Working Paper Series in Economics and Finance 315, Stockholm School of Economics.
When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-00179275. 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: (CCSD)
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.