Abstract
This paper introduces a novel framework for designing robust filters associated
with signal plus noise models having symmetric observation density. The filters
are obtained by a recursion where the innovation term is a transform of the cumulative distribution function of the residuals. The latter downweights extreme
values by construction and allows the filters to be analytically tractable. The updating scheme naturally arises as the solution of an optimization problem, where
the objective function is a continuous version of the quantile check function, formerly employed as a proper scoring function for quantiles and used to construct
robust minimum contrast estimators. Stationarity, ergodicity and invertibility are
derived under minimal assumptions and preserved under different parametric specifications. Estimation is carried out by the method of maximum likelihood and the
asymptotic theory is developed under misspecification. As an illustration, the new
filters are applied to brain scan data and compared, across Gaussian, Student-t,
Cauchy and Logistic density specifications, with alternative methods. Additional
results include a novel class of score-driven models and a subgaussian density suitable for robust filtering and modelling, arising as the infinite sum of independent
non identically distributed uniform random variables.
with signal plus noise models having symmetric observation density. The filters
are obtained by a recursion where the innovation term is a transform of the cumulative distribution function of the residuals. The latter downweights extreme
values by construction and allows the filters to be analytically tractable. The updating scheme naturally arises as the solution of an optimization problem, where
the objective function is a continuous version of the quantile check function, formerly employed as a proper scoring function for quantiles and used to construct
robust minimum contrast estimators. Stationarity, ergodicity and invertibility are
derived under minimal assumptions and preserved under different parametric specifications. Estimation is carried out by the method of maximum likelihood and the
asymptotic theory is developed under misspecification. As an illustration, the new
filters are applied to brain scan data and compared, across Gaussian, Student-t,
Cauchy and Logistic density specifications, with alternative methods. Additional
results include a novel class of score-driven models and a subgaussian density suitable for robust filtering and modelling, arising as the infinite sum of independent
non identically distributed uniform random variables.
| Original language | English |
|---|---|
| Journal | Journal of Time Series Analysis |
| ISSN | 0143-9782 |
| DOIs | |
| Publication status | E-pub / Early view - 2025 |