Doctoral thesis

Robust statistical procedures for location and scale dynamic models with applications to risk management


103 p

Thèse de doctorat: Università della Svizzera italiana, 2004 (jury note: Summa cum laude)

English In the first part of the thesis, we study the local robustness of inference procedures of the conditional location and scale parameters in a stationary time series model. We first derive optimal bounded-influence estimators for the parameters of conditional location and scale models under a conditionally Gaussian reference model. Based on these results, optimal bounded-influence versions of the classical likelihood-based tests for parametric hypotheses are then obtained. We propose a feasible and efficient algorithm for the computation of our robust estimators, which makes use of some 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 estimators and tests maintain a very high efficiency under ideal model conditions and at the same time perform very satisfactorily under several forms of departures from a conditionally normal AR(1)-ARCH(1) process. 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. In the second part of the thesis, we apply our robust inference procedures to estimate asset volatilities in order to obtain accurate risk measure predictions. A model of the GARCH family for historical portfolio returns is estimated with an efficient robust estimator. Resampling procedures are applied on standardized residuals to estimate Value at Risk measures. In some Monte Carlo simulations we show that our robust approach performs well compared to competing approaches based on non robust volatility estimation procedures. Backtesting on four stock price series show that our robust approach gives more stable Value at Risk profiles and reserve amounts than classical approaches and a similar backtesting performance.
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