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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.
(This abstract was borrowed from another version of this item.)

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  • Mancini, Loriano & Ronchetti, Elvezio & Trojani, Fabio, 2005. "Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 628-641, June.
    • Handle: RePEc:bes:jnlasa:v:100:y:2005:p:628-641
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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. Loriano Mancini & Fabio Trojani, 2011. "Robust Value at Risk Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 281-313, Spring.
    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. 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. Sonja Rieder, 2012. "Robust parameter estimation for the Ornstein–Uhlenbeck process," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(4), pages 411-436, November.
    6. Hotta, Luiz & Trucíos, Carlos, 2015. "Robust bootstrap forecast densities for GARCH models: returns, volatilities and value-at-risk," DES - Working Papers. Statistics and Econometrics. WS ws1523, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    8. Hill, Jonathan B., 2015. "Robust Generalized Empirical Likelihood for heavy tailed autoregressions with conditionally heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 135(C), pages 131-152.
    9. Lorenzo Camponovo & O. Scaillet & Fabio Trojani, 2013. "Predictability Hidden by Anomalous Observations," Swiss Finance Institute Research Paper Series 13-05, Swiss Finance Institute.
    10. Camponovo, Lorenzo & Scaillet, Olivier & Trojani, Fabio, 2012. "Robust subsampling," Journal of Econometrics, Elsevier, vol. 167(1), pages 197-210.
    11. Trojani, Fabio & Wiehenkamp, Christian & Wrampelmeyer, Jan, 2014. "Ambiguity and Reality," Working Papers on Finance 1418, University of St. Gallen, School of Finance.
    12. Tadeusz Bednarski, 2010. "Fréchet differentiability in statistical inference for time series," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(4), pages 517-528, November.
    13. Fabio Trojani, 2007. "Accurate Short-Term Yield Curve Forecasting using Functional Gradient Descent," Journal of Financial Econometrics, Oxford University Press, vol. 5(4), pages 591-623, Fall.
    14. Aguilar, Mike & Hill, Jonathan B., 2015. "Robust score and portmanteau tests of volatility spillover," Journal of Econometrics, Elsevier, vol. 184(1), pages 37-61.
    15. Bellio, Ruggero, 2007. "Algorithms for bounded-influence estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2531-2541, February.
    16. Marc Hallin & Davide La Vecchia, 2014. "Semiparametrically Efficient R-Estimation for Dynamic Location-Scale Models," Working Papers ECARES ECARES 2014-45, ULB -- Universite Libre de Bruxelles.
    17. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    18. La Vecchia, Davide & Camponovo, Lorenzo & Ferrari, Davide, 2015. "Robust heart rate variability analysis by generalized entropy minimization," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 137-151.
    19. Elvezio Ronchetti, 2016. "Discussion of the Paper “Asymptotic Theory of Outlier Detection Algorithms for Linear Time Series Regression Models” by Johansen & Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 368-370, June.
    20. Pierre‐Yves Deléamont & Elvezio Ronchetti, 2022. "Robust inference with censored survival data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1496-1533, December.
    21. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.

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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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