Wavelet-variance-based estimation for composite stochastic processes

Stéphane Guerrier, Jan Skaloud, Yannick Stebler, Maria Pia Victoria-Feser

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

This article presents a new estimation method for the parameters of a time series model.We consider here composite Gaussian processes 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 offers an alternative to classical estimation based on the likelihood, that is straightforward to implement and often the only feasible estimation method with complex models. The estimator furnishes results as the optimization of a criterion based on a standardized distance between the sample wavelet variances (WV) estimates and the model-basedWV. Indeed, the WV provides a decomposition of the variance process through different scales, so that they contain the information about different features of the stochastic model. We derive the asymptotic properties of the proposed estimator for inference and perform a simulation study to compare our estimator to the MLE and the LSE with different models. We also set sufficient conditions on composite models 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 first order Gauss-Markov processes by means of a sample of over 800,000 issued from gyroscopes that compose inertial navigation systems. Supplementary materials for this article are available online.

Original languageEnglish (US)
Pages (from-to)1021-1030
Number of pages10
JournalJournal of the American Statistical Association
Volume108
Issue number503
DOIs
StatePublished - Dec 16 2013

Fingerprint

Stochastic Processes
Wavelets
Composite
Estimator
Gaussian Process
Inertial Navigation System
Gyroscope
Time Series Models
Model
Estimate
Markov Process
Gauss
Asymptotic Properties
Stochastic Model
Likelihood
Time series
Stochastic processes
Simulation Study
Verify
First-order

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Guerrier, Stéphane ; Skaloud, Jan ; Stebler, Yannick ; Victoria-Feser, Maria Pia. / Wavelet-variance-based estimation for composite stochastic processes. In: Journal of the American Statistical Association. 2013 ; Vol. 108, No. 503. pp. 1021-1030.
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Wavelet-variance-based estimation for composite stochastic processes. / Guerrier, Stéphane; Skaloud, Jan; Stebler, Yannick; Victoria-Feser, Maria Pia.

In: Journal of the American Statistical Association, Vol. 108, No. 503, 16.12.2013, p. 1021-1030.

Research output: Contribution to journalArticle

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