A new robust and statistically efficient estimator for ARMA models called thebounded influence propagation (BIP) {\tau}-estimator is proposed. The estimatorincorporates an auxiliary model, which prevents the propagation of outliers.Strong consistency and asymptotic normality of the estimator for ARMA modelsthat are driven by independently and identically distributed (iid) innovationswith symmetric distributions are established. To analyze the infinitesimaleffect of outliers on the estimator, the influence function is derived andcomputed explicitly for an AR(1) model with additive outliers. To obtainestimates for the AR(p) model, a robust Durbin-Levinson type and aforward-backward algorithm are proposed. An iterative algorithm to robustlyobtain ARMA(p,q) parameter estimates is also presented. The problem of findinga robust initialization is addressed, which for orders p+q>2 is a non-trivialmatter. Numerical experiments are conducted to compare the finite sampleperformance of the proposed estimator to existing robust methodologies fordifferent types of outliers both in terms of average and of worst-caseperformance, as measured by the maximum bias curve. To illustrate the practicalapplicability of the proposed estimator, a real-data example of outliercleaning for R-R interval plots derived from electrocardiographic (ECG) data isconsidered. The proposed estimator is not limited to biomedical applications,but is also useful in any real-world problem whose observations can be modeledas an ARMA process disturbed by outliers or impulsive noise.
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