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

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  • Mancini, Loriano
  • Ronchetti, Elvezio
  • Trojani, Fabio

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

Article provided by American Statistical Association in its journal Journal of the American Statistical Association.

Volume (Year): 100 (2005)
Issue (Month): (June)
Pages: 628-641

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Handle: RePEc:bes:jnlasa:v:100:y:2005:p:628-641

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  1. Franco Peracchi, 1988. "Robust M-Estimators," UCLA Economics Working Papers 477, UCLA Department of Economics.
  2. 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.
  3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  4. Shinichi Sakata & Halbert White, 1998. "High Breakdown Point Conditional Dispersion Estimation with Application to S&P 500 Daily Returns Volatility," Econometrica, Econometric Society, vol. 66(3), pages 529-568, May.
  5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  6. Krishnakumar, J. & Ronchetti, E., 1997. "Robust estimators for simultaneous equations models," Journal of Econometrics, Elsevier, vol. 78(2), pages 295-314, June.
  7. 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.
  8. Ortelli, Claudio & Trojani, Fabio, 2005. "Robust efficient method of moments," Journal of Econometrics, Elsevier, vol. 128(1), pages 69-97, September.
  9. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
  10. Gagliardini, Patrick & Trojani, Fabio & Urga, Giovanni, 2005. "Robust GMM tests for structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 139-182.
  11. Gourieroux Christian & Monfort Alain & Trognon A, 1981. "Pseudo maximum likelihood methods : theory," CEPREMAP Working Papers (Couverture Orange) 8129, CEPREMAP.
  12. Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
  13. 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.
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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. Gagliardini, Patrick & Trojani, Fabio & Urga, Giovanni, 2005. "Robust GMM tests for structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 139-182.
  3. La Vecchia, Davide & Trojani, Fabio, 2010. "Infinitesimal Robustness for Diffusions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 703-712.
  4. Sonja Rieder, 2012. "Robust parameter estimation for the Ornstein–Uhlenbeck process," Statistical Methods and Applications, Springer, vol. 21(4), pages 411-436, November.
  5. Boudt, Kris & Croux, Christophe, 2010. "Robust M-estimation of multivariate GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2459-2469, November.
  6. Lorenzo Camponovo & Olivier Scaillet & Fabio Trojani, 2006. "Robust Subsampling," Swiss Finance Institute Research Paper Series 06-33, Swiss Finance Institute.
  7. Tadeusz Bednarski, 2010. "Fréchet differentiability in statistical inference for time series," Statistical Methods and Applications, Springer, vol. 19(4), pages 517-528, November.
  8. 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.
  9. Bellio, Ruggero, 2007. "Algorithms for bounded-influence estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2531-2541, February.

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