A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences
Abstract
We propose a TAR(3,1)-GARCH(1,1) model able to describe two different types of extreme events: a first type generated by large uncertainty regimes and a second type where extremes come from isolated dread/joy events. The novelty of this model resides on the definition of the regimes, motivated by the occurrence of extreme values, and of the threshold variable, defined by the shock affecting the process one period lagged. The model is able to uncover dependence and clustering of extremes in high and low volatility periods. A Wald type test to detect nonlinearities on the conditional mean process defined by an unobservable threshold variable is introduced. In the empirical application, we find evidence of predictability for extreme returns on SPDR S&P500 fund during the recent crisis period, July 2008 to March 2011. This finding seems to support the presence of some persistence and mean reversion in the dynamics of returns after the occurrence of extreme shocks.Download Info
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.As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic Info
Article provided by De Gruyter in its journal Studies in Nonlinear Dynamics & Econometrics.
Volume (Year): 16 (2012)
Issue (Month): 3 ()
Pages: 3
Contact details of provider:
Web page: http://www.degruyter.com
Order Information:
Web: http://www.degruyter.com/view/j/snde
Related research
Keywords: asymmetries; financial crises; hypothesis testing; nonlinearities; threshold models;Other versions of this item:
- Martínez Ibáñez, Oscar & Olmo, José, 2008. "A nonlinear threshold model for the dependence of extremes of stationary sequences," Working Papers 2072/5361, Universitat Rovira i Virgili, Department of Economics.
- Martinez, O. & Olmo, J., 2008. "A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences," Working Papers 08/08, Department of Economics, City University London.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
References
References listed on IDEASPlease 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.:
- Shiqing Ling & Michael McAleer, 2001.
"Asymptotic Theory for a Vector ARMA-GARCH Model,"
ISER Discussion Paper
0549, Institute of Social and Economic Research, Osaka University.
- 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.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- González, M. & Gonzalo, Jesús, . "Threshold unit root models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/6214, Universidad Carlos III de Madrid.
- Gonzalo, Jesus & Martinez, Oscar, 2006.
"Large shocks vs. small shocks. (Or does size matter? May be so.),"
Journal of Econometrics,
Elsevier, vol. 135(1-2), pages 311-347.
- Gonzalo, Jesús & Martínez, Oscar, . "Large shocks vs. small shocks. (Or does size matter? May be so.)," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/3229, Universidad Carlos III de Madrid.
- Dennis Kristensen, 2009. "On stationarity and ergodicity of the bilinear model with applications to GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 125-144, 01.
- Donald W.K. Andrews & Werner Ploberger, 1992.
"Optimal Tests When a Nuisance Parameter Is Present Only Under the Alternative,"
Cowles Foundation Discussion Papers
1015, Cowles Foundation for Research in Economics, Yale University.
- Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
- Stephen J. Taylor, 1994. "Modeling Stochastic Volatility: A Review And Comparative Study," Mathematical Finance, Wiley Blackwell, vol. 4(2), pages 183-204.
- Gonzalo, Jesus & Pitarakis, Jean-Yves, 2002.
"Estimation and model selection based inference in single and multiple threshold models,"
Journal of Econometrics,
Elsevier, vol. 110(2), pages 319-352, October.
- Gonzalo, Jesús & Pitarakis, Jean-Yves, . "Estimation and model selection based inference in single and multiple threshold models," Open Access publications from Universidad Carlos III de Madrid info:hdl:10016/766, Universidad Carlos III de Madrid.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1995.
"Multivariate Stochastic Variance Models,"
Open Access publications from Universidad Carlos III de Madrid
info:hdl:10016/4783, Universidad Carlos III de Madrid.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Engle, Robert F & Smith, Aaron, 1998.
"Stochastic Permanent Breaks,"
University of California at San Diego, Economics Working Paper Series
qt99v0s0zx, Department of Economics, UC San Diego.
- Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November.
- Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
Citations
Lists
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.Statistics
Access and download statisticsCorrections
When requesting a correction, please mention this item's handle: RePEc:bpj:sndecm:v:16:y:2012:i:3:n:3For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla).
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.

