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Mallows’ quasi-likelihood estimation for log-linear Poisson autoregressions. (English) Zbl 1349.62409

Summary: We consider the problems of robust estimation and testing for a log-linear model with feedback for the analysis of count time series. We study inference for contaminated data with transient shifts, level shifts and additive outliers. It turns out that the case of additive outliers deserves special attention. We propose a robust method for estimating the regression coefficients in the presence of interventions. The resulting robust estimators are asymptotically normally distributed under some regularity conditions. A robust score type test statistic is also examined. The methodology is applied to real and simulated data.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62F35 Robustness and adaptive procedures (parametric inference)
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