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Nonparametric autoregression with multiplicative volatility and additive mean

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  • Yang, Lijian
  • Härdle, Wolfgang
  • Nielsen, Jens P.

Abstract

For over a decade, nonparametric modelling has been successfully applied to study nonlinear structures in financial time series. It is well known that the usual nonparametric models often have less than satisfactory performance when dealing with more than one lag. When the mean has an additive structure, however, better estimation methods are available which fully exploit such a structure. Although in the past such nonparametric applications had been focused more on the estimation of the conditional mean, it is equally if not more important to measure the future risk of the series along with the mean. For the volatility function, i.e., the conditional variance given the past, a multiplicative structure is more appropriate than an additive one, as the volatility is a positive scale function and a multiplicative model provides a better interpretation of each lagged value's influence on such a function. In this paper we consider the joint estimation of both the additive mean and the multiplicative volatility. The technique used is marginally integrated local polynomial estimation. The procedure is applied to the DEM/USD (Deutsche Mark/US Dollar) daily exchange returns. --

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Bibliographic Info

Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 1998,107.

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Date of creation: 1998
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Handle: RePEc:zbw:sfb373:1998107

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Related research

Keywords: Additive Mean; Geometric Ergodicity; Geometric Mixing; Local Polynomial Regression; Marginal Integration; Multiplicative Volatility; Stationary Probability Density;

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References

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  1. Wolfgang HÄRDLE & R. CHEN, 1995. "Nonparametric Time Series Analysis, a selectiv review with examples," SFB 373 Discussion Papers 1995,14, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Wolfgang HÄRDLE & A. TSYBAKOV & L. YANG, 1996. "Nonparametric Vector Autoregression," SFB 373 Discussion Papers 1996,61, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Tschernig, Rolf & Yang, Lijian, 1997. "Nonparametric lag selection for time series," SFB 373 Discussion Papers 1997,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  4. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
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Cited by:
  1. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
  2. Siegfried Heiler, 1999. "A Survey on Nonparametric Time Series Analysis," CoFE Discussion Paper 99-05, Center of Finance and Econometrics, University of Konstanz.
  3. Mohamed Chikhi & Claude Diebolt, 2006. "Nonparametric Analysis of Financial Time Series by the Kernel Methodology," Working Papers 06-11, Association Française de Cliométrie (AFC).
  4. Francesco Audrino & Peter Bühlmann, 2009. "Splines for financial volatility," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 655-670.
  5. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 663-690, September.
  6. HARDLE, Wolfgang & HAFNER, Christian M., . "Discrete time option pricing with flexible volatility estimation," CORE Discussion Papers RP -1439, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Neumann, Michael H., 1997. "On robustness of model-based bootstrap schemes in nonparametric time series analysis," SFB 373 Discussion Papers 1997,88, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  8. Siegfried Heiler, 1999. "A Survey on Nonparametric Time Series Analysis," Finance 9904005, EconWPA.
  9. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
  10. Oliver Linton & Pedro Gozalo, 1995. "Testing Additivity in Generalized Nonparametric Regression Models," Cowles Foundation Discussion Papers 1106, Cowles Foundation for Research in Economics, Yale University.
  11. Yang, Lijian, 2006. "A semiparametric GARCH model for foreign exchange volatility," Journal of Econometrics, Elsevier, vol. 130(2), pages 365-384, February.
  12. Buhlmann, Peter & McNeil, Alexander J., 2002. "An algorithm for nonparametric GARCH modelling," Computational Statistics & Data Analysis, Elsevier, vol. 40(4), pages 665-683, October.
  13. Tschernig, Rolf & Yang, Lijian, 1997. "Nonparametric lag selection for time series," SFB 373 Discussion Papers 1997,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.

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