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

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  1. Wolfgang HÄRDLE & R. CHEN, 1995. "Nonparametric Time Series Analysis, a selectiv review with examples," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1995,14, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  2. Wolfgang HÄRDLE & A. TSYBAKOV, 1995. "Local Polynomial Estimators of the Volatility Function in Nonparametric Autoregression," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1995,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  3. Drost, F.C. & Nijman, T.E., 1992. "Temporal aggregation of GARCH processes," Discussion Paper, Tilburg University, Center for Economic Research 1992-40, Tilburg University, Center for Economic Research.
  4. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 9(4), pages 345-59, October.
  5. Wolfgang HÄRDLE & A. TSYBAKOV & L. YANG, 1996. "Nonparametric Vector Autoregression," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1996,61, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  6. Tschernig, Rolf & Yang, Lijian, 1997. "Nonparametric lag selection for time series," SFB 373 Discussion Papers, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes 1997,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  7. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
  8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  9. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 159-199.
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