Mixed \(\ell_2\) and \(\ell_1\)-norm regularization for adaptive detrending with ARMA modeling. (English) Zbl 1393.93084
Summary: In this paper, the problem of detrending a time series and/or estimating a wandering baseline is addressed. We propose a new methodology that adaptively minimizes different regularized cost functions by introducing an ARMA model of the underlying trend. Mixed \(\ell_1/\ell_2\)-norm penalty functions are taken into consideration and novel RLS and LMS solutions are derived for the model parameters estimation. The proposed methods are applied to typical trend estimation/removal problems that can be found in the analysis of economic time series or biomedical signal acquisition. Comparisons with standard noncausal filtering techniques are also presented.
MSC:
| 93C70 | Time-scale analysis and singular perturbations in control/observation systems |
| 37M10 | Time series analysis of dynamical systems |
| 93E20 | Optimal stochastic control |
| 90C15 | Stochastic programming |
| 93C40 | Adaptive control/observation systems |
Keywords:
detrending a time series; adaptive detrending with ARMA modeling; penalty functions; noncausal filtering techniquesReferences:
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