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Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models

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  • Loriano Mancini

    ()

  • Elvezio Ronchetti

    ()

  • Fabio Trojani

    ()

Abstract

This paper studies the local robustness of estimators and tests for the conditional location and scale parameters in a strictly stationary time series model. We first derive optimal bounded-influence estimators for such settings under a conditionally Gaussian reference model. Based on these results, optimal bounded-influence versions of the classical likelihood-based tests for parametric hypotheses are obtained. We propose a feasible and efficient algorithm for the computation of our robust estimators, which makes use of analytical Laplace approximations to estimate the auxiliary recentering vectors ensuring Fisher consistency in robust estimation. This strongly reduces the necessary computation time by avoiding the simulation of multidimensional integrals, a task that has typically to be addressed in the robust estimation of nonlinear models for time series. In some Monte Carlo simulations of an AR(1)-ARCH(1) process we show that our robust procedures maintain a very high efficiency under ideal model conditions and at the same time perform very satisfactorily under several forms of departure from conditional normality. On the contrary, classical Pseudo Maximum Likelihood inference procedures are found to be highly inefficient under such local model misspecifications. These patterns are confirmed by an application to robust testing for ARCH.

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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 2005 with number 2005-01.

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Length: 33 pages
Date of creation: Jan 2005
Date of revision:
Handle: RePEc:usg:dp2005:2005-01

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  1. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
  2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  3. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
  4. Franco Peracchi, 1988. "Robust M-Estimators," UCLA Economics Working Papers 477, UCLA Department of Economics.
  5. Gagliardini, Patrick & Trojani, Fabio & Urga, Giovanni, 2005. "Robust GMM tests for structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 139-182.
  6. Gourieroux, C. & Monfort, A., 1989. "A General Framework for Testing a Null Hypothesis in a “Mixed” Form," Econometric Theory, Cambridge University Press, vol. 5(01), pages 63-82, April.
  7. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  8. Ortelli, Claudio & Trojani, Fabio, 2005. "Robust efficient method of moments," Journal of Econometrics, Elsevier, vol. 128(1), pages 69-97, September.
  9. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
  10. Krishnakumar, J. & Ronchetti, E., 1997. "Robust estimators for simultaneous equations models," Journal of Econometrics, Elsevier, vol. 78(2), pages 295-314, June.
  11. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-74, May-June.
  12. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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Citations

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Cited by:
  1. Ortelli, Claudio & Trojani, Fabio, 2005. "Robust efficient method of moments," Journal of Econometrics, Elsevier, vol. 128(1), pages 69-97, September.
  2. Fabio Trojani, 2007. "Accurate Short-Term Yield Curve Forecasting using Functional Gradient Descent," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(4), pages 591-623, Fall.
  3. Boudt, Kris & Croux, Christophe, 2007. "Robust M-estimation of multivariate conditionally heteroscedastic time series models with elliptical innovations," Open Access publications from Katholieke Universiteit Leuven urn:hdl:123456789/175500, Katholieke Universiteit Leuven.
  4. Boudt, Kris & Croux, Christophe, 2010. "Robust M-estimation of multivariate GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2459-2469, November.
  5. Bellio, Ruggero, 2007. "Algorithms for bounded-influence estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2531-2541, February.
  6. Gagliardini, Patrick & Trojani, Fabio & Urga, Giovanni, 2005. "Robust GMM tests for structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 139-182.
  7. Loriano Mancini & Fabio Trojani, 2005. "Robust Value at Risk Prediction," Swiss Finance Institute Research Paper Series 07-31, Swiss Finance Institute, revised Oct 2007.
  8. Tadeusz Bednarski, 2010. "Fréchet differentiability in statistical inference for time series," Statistical Methods and Applications, Springer, vol. 19(4), pages 517-528, November.

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