|Stochastic Systems Group|
We propose a new approach to the robust estimation of a mixed autoregressive and moving average (ARMA) model, or a spatio-temporal autoregressive (STAR) model. This approach is based on the indirect inference method which originally was proposed for models with an intractable likelihood function. The estimation algorithm proposed for the ARMA model is based on an auxiliary autoregressive model whose parameters are first estimated on the observed time series and then on data simulated from the ARMA model. To simulate data the parameters of the ARMA model have to be set. By varying these we can minimize a distance between the simulation-based and the observation-based auxiliary estimate. The argument of the minimum yields then an estimator for the parameterization of the ARMA model. This simulation-based estimation procedure inherits the properties of the auxiliary model estimator. For instance, robustness is achieved with GM-estimators. In contrast with existing robust estimation procedures, consistency and asymptotic normality of the introduced estimator can be derived, as well as its influence function and breakdown point. In a small sample Monte Carlo study it is found that the new estimator performs equally well than existing procedures. Furthermore, with two real examples, we have also been able to compare the proposed inferential method with two different approaches based on outliers detection. Our particular simulation-based estimation algorithm also implicitly introduces a general-purpose robust estimation methodology for models for which no classical robust estimation criterion is available neither in closed form nor algorithmically. For instance, we derive the influence function in whole generality. Finally, we extend our technique to the robust estimation of STAR models, using a quadrant autoregression (QAR) as an auxiliary model.
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