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

Journal of the American Statistical Association, Vol. 100, No. 470, pp. 628-641, June 2005

34 Pages Posted: 29 Jul 2003

See all articles by Loriano Mancini

Loriano Mancini

USI Lugano - Institute of Finance; Swiss Finance Institute

Fabio Trojani

Swiss Finance Institute; University of Geneva

Elvezio Ronchetti

University of Geneva - Research Center for Statistics

Date Written: January 2004

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.

Keywords: Time series models, M-estimators, influence function, robust estimation and testing

JEL Classification: C12, C13, C14, C22

Suggested Citation

Mancini, Loriano and Trojani, Fabio and Ronchetti, Elvezio, Optimal Conditionally Unbiased Bounded-Influence Inference in Dynamic Location and Scale Models (January 2004). Journal of the American Statistical Association, Vol. 100, No. 470, pp. 628-641, June 2005 . Available at SSRN: https://ssrn.com/abstract=414060 or http://dx.doi.org/10.2139/ssrn.414060

Loriano Mancini (Contact Author)

USI Lugano - Institute of Finance ( email )

Via Giuseppe Buffi 6
6904 Lugano, CH-6904
Switzerland
+41 (0)91 912 46 47 (Fax)

HOME PAGE: http://www.people.usi.ch/mancil/

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

Fabio Trojani

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

University of Geneva ( email )

Geneva
Switzerland

Elvezio Ronchetti

University of Geneva - Research Center for Statistics ( email )

Blv. Pont d'Arve 40
1211 Geneva 4
Switzerland

HOME PAGE: http://www.unige.ch/ses/metri/ronchetti/

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