Splines for Financial Volatility
AbstractWe propose a flexible GARCH-type model for the prediction of volatility in financial time series. The approach relies on the idea of using multivariate B-splines of lagged observations and volatilities. Estimation of such a B-spline basis expansion is constructed within the likelihood framework for non-Gaussian observations. As the dimension of the B-spline basis is large, i.e. many parameters, we use regularized and sparse model fitting with a boosting algorithm. Our method is computationally attractive and feasible for large dimensions. We demonstrate its strong predictive potential for financial volatility on simulated and real data, also in comparison to other approaches, and we present some supporting asymptotic arguments.
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 InfoPaper provided by Department of Economics, University of St. Gallen in its series University of St. Gallen Department of Economics working paper series 2007 with number 2007-11.
Length: 25 pages
Date of creation: Apr 2007
Date of revision:
Boosting; B-splines; Conditional variance; Financial time series; GARCH model; Volatility;
Other versions of this item:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-05-12 (All new papers)
- NEP-ECM-2007-05-12 (Econometrics)
- NEP-ETS-2007-05-12 (Econometric Time Series)
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.:
- Robert F. Engle & Jose Gonzalo Rangel, 2005. "The Spline GARCH Model for Unconditional Volatility and its Global Macroeconomic Causes," Working Papers 2005/13, Czech National Bank, Research Department.
- Asger Lunde & Peter R. Hansen, 2005.
"A forecast comparison of volatility models: does anything beat a GARCH(1,1)?,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 20(7), pages 873-889.
- Asger Lunde & Peter Reinhard Hansen, 2001. "A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)?," Working Papers 2001-04, Brown University, Department of Economics.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001.
"Modeling and Forecasting Realized Volatility,"
Center for Financial Institutions Working Papers
01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
- Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
- 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.
- Gourieroux Christian & Monfort Alain, 1991.
"Qualitative threshold arch models,"
CEPREMAP Working Papers (Couverture Orange)
- 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.
- Tom Doan, . "RATS programs to replicate Baillie, Bollerslev, Mikkelson FIGARCH results," Statistical Software Components RTZ00009, Boston College Department of Economics.
- Francesco Audrino, 2005. "Local Likelihood for non-parametric ARCH(1) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 251-278, 03.
- Hardle, W. & Tsybakov, A., 1997.
"Local polynomial estimators of the volatility function in nonparametric autoregression,"
Journal of Econometrics,
Elsevier, vol. 81(1), pages 223-242, November.
- Wolfgang HÄRDLE & A. TSYBAKOV, 1995. "Local Polynomial Estimators of the Volatility Function in Nonparametric Autoregression," SFB 373 Discussion Papers 1995,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- L. YANG & Wolfgang HÄRDLE, 1996.
"Nonparametric Autoregression with Multiplicative Volatility and Additive Mean,"
SFB 373 Discussion Papers
1996,62, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Yang, Lijian & Härdle, Wolfgang & Nielsen, Jens P., 1998. "Nonparametric autoregression with multiplicative volatility and additive mean," SFB 373 Discussion Papers 1998,107, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Christan Francq & Jean-Michel Zakoian, 2012.
"Optimal Predictions of Powers of Conditionally Heteroskedastic Processes,"
2012-17, Centre de Recherche en Economie et Statistique.
- Christian Francq & Jean-Michel Zakoïan, 2013. "Optimal predictions of powers of conditionally heteroscedastic processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 345-367, 03.
- Francq, Christian & Zakoian, Jean-Michel, 2010. "Optimal predictions of powers of conditionally heteroskedastic processes," MPRA Paper 22155, University Library of Munich, Germany.
- Audrino, Francesco & Meier, Pirmin, 2012. "Empirical pricing kernel estimation using a functional gradient descent algorithm based on splines," Economics Working Paper Series 1210, University of St. Gallen, School of Economics and Political Science.
- Ozer Ozdemir & Memmedaga Memmedli & Akhlitdin Nizamitdinov, 2013. "ANN Models and Bayesian Spline Models for Analysis of Exchange Rates and Gold Price," International Econometric Review (IER), Econometric Research Association, vol. 5(2), pages 53-69, September.
- Souhaib Ben Taieb & Rob J Hyndman, 2014. "Boosting multi-step autoregressive forecasts," Monash Econometrics and Business Statistics Working Papers 13/14, Monash University, Department of Econometrics and Business Statistics.
- VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," CORE Discussion Papers 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Nikolay Robinzonov & Gerhard Tutz & Torsten Hothorn, 2012. "Boosting techniques for nonlinear time series models," AStA Advances in Statistical Analysis, Springer, vol. 96(1), pages 99-122, January.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Joerg Baumberger).
If references are entirely missing, you can add them using this form.