*Wavelet Variance based Estimation of Latent Time Series Models*

 *Stéphane* *Guerrier*

 *Research Center for Statistics*

 *University of Geneva*

 *Johnson Center **G19-Gold Room*

*4400 University Drive, Fairfax, VA 22030*

 *Time: 10:30 A.M. - 11:30 A.M.*

 *Date: **Wednesday**, **Jan 29**, 201**4*


This paper presents a new estimation method for the parameters of a times
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 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.

Yunpeng Zhao, PhD

Assistant Professor
Department of Statistics
Volgenau School of Engineering <[log in to unmask]>
George Mason University
Engineering Building, Room 1719, MS 4A7
4400 University Drive
Fairfax, VA 22030-4444

Phone: 703-993-1674
Email: [log in to unmask]