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Wavelet variance based estimation for composite stochastic processes

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Author Guerrier Stéphane, Stebler Yannick, Skaloud Jan, Victoria-Feser Maria-Pia,
Project Robust Prediction and Model Choice in Mixed Linear Models for the Analysis of Social Sciences Data
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Original article (peer-reviewed)

Journal Journal of the American Statistical Association
Volume (Issue) 108(503)
Page(s) 1021 - 1030
Title of proceedings Journal of the American Statistical Association

Open Access

Abstract

This paper presents a new estimation method for the parameters of a times series model. We consider here composite Gaussian pro- cesses that are the sum of independent Gaussian processes which in turn explain an important aspect of the time series, as is the case in engineering and natural sciences. The proposed estimation method oers an alternative to classical estimation based on the likelihood, that is straightforward to implement and often the only feasible es- timation method with complex models. The estimator results as the optimization of a criterion based on a standardized distance between the sample wavelet variances (WV) estimates and the model based WV. Indeed, the WV provides a decomposition of the variance process through dierent scales, so that they contain the information about dierent features of the stochastic model. We derive the asymptotic properties of the proposed estimator for inference and perform a sim- ulation study to compare our estimator to the MLE and the LSE with dierent models. We also set sucient conditions on composite mod- els for our estimator to be consistent, that are easy to verify. We use the new estimator to estimate the stochastic error's parameters of the sum of three rst order Gauss-Markov processes by means of a sample of over 800; 000 issued from gyroscopes that compose inertial navigation systems.
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