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

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 cont...

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Vydáno v:Journal of the American Statistical Association Ročník 117; číslo 540; s. 1996 - 2013
Hlavní autoři: Guerrier, Stéphane, Molinari, Roberto, Victoria-Feser, Maria-Pia, Xu, Haotian
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Taylor & Francis 02.10.2022
Taylor & Francis Ltd
Témata:
Asymptotic properties
Biology
Complexity
Data analysis
Ecology
Economic analysis
Economic models
economics
Estimation
Generalized method of wavelet moments
Inference
Large-scale time series
Normality
Outliers (statistics)
prediction
Prediction models
Property
Regression analysis
Robustness
Scale-based analysis of variance
Signal processing
Simulation
State-space models
Statistical methods
Statistics
Stochastic models
Stochastic processes
Theory and Methods
Time series
time series analysis
variance
wavelet
Wavelet variance
Large-scale time series
Signal processing
Scale-based analysis of variance
Generalized method of wavelet moments
State-space models
Wavelet variance
ISSN:0162-1459, 1537-274X, 1537-274X
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Popis
Shrnutí: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.
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Supplementary materials for this article are available online. Please go to www.tandfonline.com/r/JASA.
ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2021.1895176