Learning AR factor models

Crescente, Francesca; Falconi, Lucia; Rozzi, Federica; Ferrante, Augusto; Zorzi, Mattia

doi:10.1109/cdc42340.2020.9304289

“…may be rewritten as λT ( P ) + T (Z) W 0 0 0 and then, by Lemma 4.1, λT ( P ) + T (Z) 0. Now, we can easily rewrite (35) recalling the characterization of a symmetric positive semidefinite matrix using the Schur complement.…”

Section: The Proposed Algorithmmentioning

confidence: 99%

A Robust Approach to ARMA Factor Modeling

Falconi

¹

,

Ferrante

²

,

Zorzi

³

2024

IEEE Trans. Automat. Contr.

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This paper deals with the dynamic factor analysis problem for an ARMA process. To robustly estimate the number of factors, we construct a confidence region centered in a finite sample estimate of the underlying model which contains the true model with a prescribed probability. In this confidence region, the problem, formulated as a rank minimization of a suitable spectral density, is efficiently approximated via a trace norm convex relaxation. The latter is addressed by resorting to the Lagrange duality theory, which allows to prove the existence of solutions. Finally, a numerical algorithm to solve the dual problem is presented. The effectiveness of the proposed estimator is assessed through simulation studies both with synthetic and real data.

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“…1) The AR dynamic estimation. Given the realization y N , we estimate the p parameters of the filter a by applying the maximum likelihood estimator proposed in [27,Section II.b].…”

Section: Identification Of Arma Factor Modelsmentioning

confidence: 99%

A Robust Approach to ARMA Factor Modeling

Falconi¹,

Ferrante²,

Zorzi³

2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

This paper deals with the dynamic factor analysis problem for an ARMA process. To robustly estimate the number of factors, we construct a confidence region centered in a finite sample estimate of the underlying model which contains the true model with a prescribed probability. In this confidence region, the problem, formulated as a rank minimization of a suitable spectral density, is efficiently approximated via a trace norm convex relaxation. The latter is addressed by resorting to the Lagrange duality theory, which allows to prove the existence of solutions. Finally, a numerical algorithm to solve the dual problem is presented. The effectiveness of the proposed estimator is assessed through simulation studies both with synthetic and real data.

show abstract