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Splines for Financial Volatility

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  • Francesco Audrino

    ()

  • Peter Bühlmann

    ()

Abstract

We 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.

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Bibliographic Info

Paper 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.

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Length: 25 pages
Date of creation: Apr 2007
Date of revision:
Handle: RePEc:usg:dp2007:2007-11

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Keywords: Boosting; B-splines; Conditional variance; Financial time series; GARCH model; Volatility;

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References

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  6. 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.
  7. 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.
  8. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199.
  9. 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.
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Cited by:
  1. Christan Francq & Jean-Michel Zakoian, 2012. "Optimal Predictions of Powers of Conditionally Heteroskedastic Processes," Working Papers 2012-17, Centre de Recherche en Economie et Statistique.
  2. 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.
  3. VAN BELLEGEM, Sébastien, 2011. "Locally stationary volatility modelling," CORE Discussion Papers 2011041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. 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.
  6. 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.

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