Dynamic Functional Data Analysis with Nonparametric State Space Models
AbstractIn this article we introduce a new methodology for modeling curves with a dynamic structure, using a non-parametric approach formulated as a state space model. The non-parametric approach is based on the use of penalized splines, represented as a dynamic mixed model. This formulation can capture the dynamic evolution of curves using a limited number of latent factors, allowing a accurate fit with a limited number of parameters. We also present a new method to determine the optimal smoothing parameter through an adaptive procedure using a formulation analogous to a model of stochastic volatility. This methodology allows unifying different methodologies applied to data with a functional structure in finance. We present the advantages and limitations of this methodology through a simulation study and also comparing its predictive performance with other parametric and non-parametric methods used in financial applications using data from term structure of interest rates.
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Bibliographic InfoPaper provided by Economics Research Group, IBMEC Business School - Rio de Janeiro in its series IBMEC RJ Economics Discussion Papers with number 2012-01.
Date of creation: 16 Mar 2012
Date of revision:
Functional Data; Penalized Splines; MCMC; Bayesian non-parametric methods;
Find related papers by JEL classification:
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-03-28 (All new papers)
- NEP-ECM-2012-03-28 (Econometrics)
- NEP-ETS-2012-03-28 (Econometric Time Series)
- NEP-ORE-2012-03-28 (Operations Research)
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- Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007.
"The Affine Arbitrage-Free Class of Nelson-Siegel Term Structure Models,"
PIER Working Paper Archive
07-029, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Christensen, Jens H.E. & Diebold, Francis X. & Rudebusch, Glenn D., 2011. "The affine arbitrage-free class of Nelson-Siegel term structure models," Journal of Econometrics, Elsevier, vol. 164(1), pages 4-20, September.
- Jens H.E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The affine arbitrage-free class of Nelson-Siegel term structure models," Working Paper Series 2007-20, Federal Reserve Bank of San Francisco.
- Jens H. E. Christensen & Francis X. Diebold & Glenn D. Rudebusch, 2007. "The Affine Arbitrage-Free Class of: Nelson-Siegel Term Structure Models," NBER Working Papers 13611, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine & Duarte, Jefferson, 2003.
"Nonparametric option pricing under shape restrictions,"
Journal of Econometrics,
Elsevier, vol. 116(1-2), pages 9-47.
- Yacine Ait-Sahalia & Jefferson Duarte, 2002. "Nonparametric Option Pricing under Shape Restrictions," NBER Working Papers 8944, National Bureau of Economic Research, Inc.
- Rob J. Hyndman & Md. Shahid Ullah, 2005.
"Robust forecasting of mortality and fertility rates: a functional data approach,"
Monash Econometrics and Business Statistics Working Papers
2/05, Monash University, Department of Econometrics and Business Statistics.
- Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
- Barzanti, Luca & Corradi, Corrado, 1998. "A note on interest rate term structure estimation using tension splines," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 139-143, June.
- Hautsch, Nikolaus & Yang, Fuyu, 2012.
"Bayesian inference in a Stochastic Volatility Nelson–Siegel model,"
Computational Statistics & Data Analysis,
Elsevier, vol. 56(11), pages 3774-3792.
- Nikolaus Hautsch & Fuyu Yang, 2010. "Bayesian Inference in a Stochastic Volatility Nelson-Siegel Model," SFB 649 Discussion Papers SFB649DP2010-004, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Diebold, Francis X. & Li, Canlin, 2006.
"Forecasting the term structure of government bond yields,"
Journal of Econometrics,
Elsevier, vol. 130(2), pages 337-364, February.
- Diebold, Francis X. & Li, Canlin, 2003. "Forecasting the term structure of government bond yields," CFS Working Paper Series 2004/09, Center for Financial Studies (CFS).
- Francis X. Diebold & Canlin Li, 2002. "Forecasting the Term Structure of Government Bond Yields," Center for Financial Institutions Working Papers 02-34, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Francis X. Diebold & Canlin Li, 2003. "Forecasting the Term Structure of Government Bond Yields," NBER Working Papers 10048, National Bureau of Economic Research, Inc.
- Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
- Jarrow, Robert & Ruppert, David & Yu, Yan, 2004. "Estimating the Interest Rate Term Structure of Corporate Debt With a Semiparametric Penalized Spline Model," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 57-66, January.
- Pham, Toan M., 1998. "Estimation of the term structure of interest rates: an international perspective," Journal of Multinational Financial Management, Elsevier, vol. 8(2-3), pages 265-283, September.
- Laurini, Márcio Poletti & Hotta, Luiz Koodi, 2010.
"Bayesian extensions to Diebold-Li term structure model,"
International Review of Financial Analysis,
Elsevier, vol. 19(5), pages 342-350, December.
- Laurini, Márcio P. & Hotta, Luiz K., 2008. "Bayesian extensions to diebold-li term structure model," Insper Working Papers wpe_122, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
- Ciprian M. Crainiceanu & David Ruppert & Matthew P. Wand, . "Bayesian Analysis for Penalized Spline Regression Using WinBUGS," Journal of Statistical Software, American Statistical Association, vol. 14(i14).
- Laurini, Márcio P. & Moura, Marcelo, 2007.
"Constrained Smoothing Splines for the Term Structure of Interest Rates,"
Insper Working Papers
wpe_100, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
- Poletti Laurini, Márcio & Moura, Marcelo, 2010. "Constrained smoothing B-splines for the term structure of interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 339-350, April.
- repec:wop:humbsf:1999-54 is not listed on IDEAS
- McCulloch, J Huston, 1971.
"Measuring the Term Structure of Interest Rates,"
The Journal of Business,
University of Chicago Press, vol. 44(1), pages 19-31, January.
- Tom Doan, . "RATS program to estimate term structure with cubic splines," Statistical Software Components RTZ00019, Boston College Department of Economics.
- McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-30, June.
- Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
- Vasicek, Oldrich A & Fong, H Gifford, 1982. " Term Structure Modeling Using Exponential Splines," Journal of Finance, American Finance Association, vol. 37(2), pages 339-48, May.
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