Optimal modeling and filtering of stochastic time series for geoscience applications
type: Item
instance of: scholarly article
title: Optimal modeling and filtering of stochastic time series for geoscience applications
zbMATH Open document ID: 1299.86027
DOI: 10.1155/2013/895061
author: J. A. Rod Blais
published in: Mathematical Problems in Engineering
publication date: 2014-11-24T00:00:00Z
review text: Summary: Sequences of observations or measurements are often modeled as realizations of stochastic processes with some stationary properties in the first and second moments. However in practice, the noise biases and variances are likely to be different for different epochs in time or regions in space, and hence such stationarity assumptions are often questionable. In the case of strict stationarity with equally spaced data, the Wiener-Hopf equations can readily be solved with fast Fourier transforms (FFTs) with optimal computational efficiency. In more general contexts, covariance matrices can also be diagonalized using the Karhunen-Loève transforms (KLTs), or more generally using empirical orthogonal and biorthogonal expansions, which are unfortunately much more demanding in terms of computational efforts. In cases with increment stationarity, the mathematical modeling can be modified and generalized covariances can be used with some computational advantages. The general nonlinear solution methodology is also briefly overviewed with the practical limitations. These different formulations are discussed with special emphasis on the spectral properties of covariance matrices and illustrated with some numerical examples. General recommendations are included for practical geoscience applications.
Mathematics Subject Classification ID: 86A32
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 6372712
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/895061
OpenAlex ID: W2166175195
Wikidata QID: Q59029342
cites work: Least squares for practitioners
description: scientific article; zbMATH DE number 6372712