Latent time series models such as (the independent sum of) ARMA(p, q) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv) solutions that address (i), (ii), and (iii) simultaneously do not exist in practice. This paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. We first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator, we then develop the asymptotic properties of two-step robust estimators using the framework of the generalized method of wavelet moments (GMWM). Simulation studies illustrate the good finite sample performance of the robust GMWM estimator and applied examples highlight the practical relevance of the proposed approach.

Guerrier S., Molinari R., Victoria Feser M. P., Xu H. (2022). Robust Two-Step Wavelet-Based Inference for Time Series Models. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 117(540), 1996-2013 [10.1080/01621459.2021.1895176].

Robust Two-Step Wavelet-Based Inference for Time Series Models

Victoria Feser M. P.;
2022

Abstract

Latent time series models such as (the independent sum of) ARMA(p, q) models with additional stochastic processes are increasingly used for data analysis in biology, ecology, engineering, and economics. Inference on and/or prediction from these models can be highly challenging: (i) the data may contain outliers that can adversely affect the estimation procedure; (ii) the computational complexity can become prohibitive when the time series are extremely large; (iii) model selection adds another layer of (computational) complexity; and (iv) solutions that address (i), (ii), and (iii) simultaneously do not exist in practice. This paper aims at jointly addressing these challenges by proposing a general framework for robust two-step estimation based on a bounded influence M-estimator of the wavelet variance. We first develop the conditions for the joint asymptotic normality of the latter estimator thereby providing the necessary tools to perform (direct) inference for scale-based analysis of signals. Taking advantage of the model-independent weights of this first-step estimator, we then develop the asymptotic properties of two-step robust estimators using the framework of the generalized method of wavelet moments (GMWM). Simulation studies illustrate the good finite sample performance of the robust GMWM estimator and applied examples highlight the practical relevance of the proposed approach.
2022
Guerrier S., Molinari R., Victoria Feser M. P., Xu H. (2022). Robust Two-Step Wavelet-Based Inference for Time Series Models. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION, 117(540), 1996-2013 [10.1080/01621459.2021.1895176].
Guerrier S.; Molinari R.; Victoria Feser M. P.; Xu H.
File in questo prodotto:
File Dimensione Formato  
Robust Two-Step Wavelet-Based Inference for Time Series Models.pdf

accesso aperto

Tipo: Versione (PDF) editoriale
Licenza: Licenza per Accesso Aperto. Creative Commons Attribuzione - Non commerciale - Non opere derivate (CCBYNCND)
Dimensione 2.94 MB
Formato Adobe PDF
2.94 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/950759
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 2
social impact