Seasonal Mackey–Glass–GARCH process and short-term dynamics
AbstractThe aim of this article is the study of complex structures which are behind the short-term predictability of stock returns series. In this regard, we employ a seasonal version of the Mackey-Glass-GARCH(p,q) model, initially proposed by Kyrtsou and Terraza (2003) and generalized by Kyrtsou (2005, 2006). It has either negligible or significant autocorrelations in the conditional mean, and a rich structure in the conditional variance. To reveal short or long memory components and non-linear structures in the French Stock Exchange (CAC40) returns series, we apply the test of Geweke and Porter-Hudak (1983), the Brock et al. (1996) and Dechert (1995) tests, the correlation-dimension method of Grassberger and Procaccia (1983), the Lyapunov exponents method of Gencay and Dechert (1992), and the Recurrence Quantification Analysis introduced by Webber and Zbilut (1994). As a confirmation procedure of the dynamics generating future movements in CAC40, we forecast the return series using a seasonal Mackey-Glass-GARCH(1,1) model. The interest of the forecasting exercise is found in the inclusion of high-dimensional non-linearities in the mean equation of returns.
Download InfoIf 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.
Bibliographic InfoArticle provided by Springer in its journal Empirical Economics.
Volume (Year): 38 (2010)
Issue (Month): 2 (April)
Contact details of provider:
Postal: Stumpergasse 56, A-1060 Vienna
Phone: ++43 - (0)1 - 599 91 - 0
Fax: ++43 - (0)1 - 599 91 - 555
Web page: http://link.springer.de/link/service/journals/00181/index.htm
More information through EDIRC
Other versions of this item:
- Catherine Kyrtsou & Michel Terraza, 2008. "Seasonal Mackey-Glass-GARCH process and short-term dynamics," Discussion Paper Series 2008_09, Department of Economics, University of Macedonia, revised Sep 2008.
- C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G - Financial Economics
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.:
- Strozzi, Fernanda & Zaldı́var, José-Manuel & Zbilut, Joseph P, 2002. "Application of nonlinear time series analysis techniques to high-frequency currency exchange data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 312(3), pages 520-538.
- 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.
- Cars H. Hommes, 2005.
"Heterogeneous Agent Models in Economics and Finance,"
Tinbergen Institute Discussion Papers
05-056/1, Tinbergen Institute.
- Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186 Elsevier.
- Catherine Kyrtsou & Michel Terraza, 2003. "Is it Possible to Study Chaotic and ARCH Behaviour Jointly? Application of a Noisy Mackey–Glass Equation with Heteroskedastic Errors to the Paris Stock Exchange Returns Series," Computational Economics, Society for Computational Economics, vol. 21(3), pages 257-276, June.
- Jorge Belaire-Franch, & Dulce Contreras & Lorena Tordera-Lledo, 2002. "Assessing Non-Linear Structures in Real Exchange Rates Using Recurrence Plot Strategies," Computing in Economics and Finance 2002 239, Society for Computational Economics.
- Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
- Kyrtsou, Catherine & Malliaris, Anastasios G., 2009. "The impact of information signals on market prices when agents have non-linear trading rules," Economic Modelling, Elsevier, vol. 26(1), pages 167-176, January.
- William A. Brock & David A. Hsieh & Blake LeBaron, 1992.
"Nonlinear Dynamics, Chaos, and Instability - Unix version,"
MIT Press Books,
The MIT Press,
edition 1, volume 1, number 0262521725.
- Tom Doan, . "BDSTEST: RATS procedure to compute Brock-Decher-Scheinkman test for i.i.d," Statistical Software Components RTS00016, Boston College Department of Economics.
- Catherine Kyrtsou & Walter C. Labys & Michel Terraza, 2004. "Noisy chaotic dynamics in commodity markets," Empirical Economics, Springer, vol. 29(3), pages 489-502, 09.
- 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 542-47, August.
- Malliaris, A. G. & Stein, Jerome L., 1999. "Methodological issues in asset pricing: Random walk or chaotic dynamics," Journal of Banking & Finance, Elsevier, vol. 23(11), pages 1605-1635, November.
- repec:att:wimass:9621 is not listed on IDEAS
- Carl Chiarella & Roberto Dieci & Laura Gardini, 2001. "Speculative Behaviour and Complex Asset Price Dynamics," Research Paper Series 49, Quantitative Finance Research Centre, University of Technology, Sydney.
- Kyrtsou, Catherine & Labys, Walter C., 2007. "Detecting positive feedback in multivariate time series: The case of metal prices and US inflation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 227-229.
- Lux, Thomas, 1995. "Herd Behaviour, Bubbles and Crashes," Economic Journal, Royal Economic Society, vol. 105(431), pages 881-96, July.
- Brock, William A. & Hommes, Cars H., 1998.
"Heterogeneous beliefs and routes to chaos in a simple asset pricing model,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 22(8-9), pages 1235-1274, August.
- Chen, Shu-Heng & Lux, Thomas & Marchesi, Michele, 2001.
"Testing for non-linear structure in an artificial financial market,"
Journal of Economic Behavior & Organization,
Elsevier, vol. 46(3), pages 327-342, November.
- Shu-Heng Chen & Thomas Lux & Michele Marchesi, 1999. "Testing for Non-Linear Structure in an Artificial Financial Market," Discussion Paper Serie B 447, University of Bonn, Germany.
- Kyrtsou, Catherine & Labys, Walter C., 2006. "Evidence for chaotic dependence between US inflation and commodity prices," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 256-266, March.
- Belaire-Franch, Jorge, 2004. "Testing for non-linearity in an artificial financial market: a recurrence quantification approach," Journal of Economic Behavior & Organization, Elsevier, vol. 54(4), pages 483-494, August.
- Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
- Gaunersdorfer, Andrea, 2000. "Endogenous fluctuations in a simple asset pricing model with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 24(5-7), pages 799-831, June.
- Catherine Kyrtsou & Costas Vorlow, 2008.
"Modelling non-linear comovements between time series,"
2008_01, Durham University Business School.
- Kyrtsou, Catherine & Vorlow, Costas, 2009. "Modelling non-linear comovements between time series," Journal of Macroeconomics, Elsevier, vol. 31(1), pages 200-211, March.
- Hommes, Cars H. & Manzan, Sebastiano, 2006. "Comments on "Testing for nonlinear structure and chaos in economic time series"," Journal of Macroeconomics, Elsevier, vol. 28(1), pages 169-174, March.
- Kyrtsou, Catherine & Terraza, Michel, 2002. "Stochastic chaos or ARCH effects in stock series?: A comparative study," International Review of Financial Analysis, Elsevier, vol. 11(4), pages 407-431.
- Beller, Kenneth & Nofsinger, John R, 1998. "On Stock Return Seasonality and Conditional Heteroskedasticity," Journal of Financial Research, Southern Finance Association & Southwestern Finance Association, vol. 21(2), pages 229-46, Summer.
- Richard Ashley, 2010. "On the Origins of Conditional Heteroscedasticity in Time Series," Working Papers e07-23, Virginia Polytechnic Institute and State University, Department of Economics.
- Nguyen, Dung Tien, 2012. "Mackey–Glass equation driven by fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5465-5472.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Guenther Eichhorn) or (Christopher F Baum).
If references are entirely missing, you can add them using this form.