Wavelet-Variance-Based Estimation for Composite Stochastic Processes

• 成果类型: Article
• 署名作者: Guerrier, Stephane; Skaloud, Jan; Stebler, Yannick; Victoria-Feser, Maria-Pia
• 署名单位: University of Geneva; Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2013.799920
• 发表日期: 2013
• 页码: 1021-1030
• 关键词: time-series; allan-variance

摘要

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-based WV. 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.