Automatic Autocorrelation and Spectral Analysis

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Springer Science & Business Media, Aug 2, 2006 - Technology & Engineering - 298 pages

Automatic Autocorrelation and Spectral Analysis gives random data a language to communicate the information they contain objectively.

In the current practice of spectral analysis, subjective decisions have to be made all of which influence the final spectral estimate and mean that different analysts obtain different results from the same stationary stochastic observations. Statistical signal processing can overcome this difficulty, producing a unique solution for any set of observations but that solution is only acceptable if it is close to the best attainable accuracy for most types of stationary data.

Automatic Autocorrelation and Spectral Analysis describes a method which fulfils the near-optimal-solution criterion. It takes advantage of greater computing power and robust algorithms to produce enough models to be sure of providing a suitable candidate for given data. Improved order selection quality guarantees that one of the best (and often the best) will be selected automatically. The data themselves suggest their best representation but should the analyst wish to intervene, alternatives can be provided. Written for graduate signal processing students and for researchers and engineers using time series analysis for practical applications ranging from breakdown prevention in heavy machinery to measuring lung noise for medical diagnosis, this text offers:

  • tuition in how power spectral density and the autocorrelation function of stochastic data can be estimated and interpreted in time series models;
  • extensive support for the MATLAB® ARMAsel toolbox;
  • applications showing the methods in action;
  • appropriate mathematics for students to apply the methods with references for those who wish to develop them further.

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Basic Concepts
Periodogram and Lagged Product Autocorrelation 29
ARMA Theory
Relations for Time Series Models 89
Estimation of Time Series Models
AR Order Selection 167
MA and ARMA Order Selection
ARMASA Toolbox with Applications
Advanced Topics in Time Series Estimation
Index 295

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About the author (2006)

Piet M.T. Broersen received the Ph.D. degree in 1976, from the Delft University of Technology in the Netherlands.

He is currently with the Department of Multi-scale Physics at TU Delft. His main research interest is in automatic identification on statistical grounds. He has developed a practical solution for the spectral and autocorrelation analysis of stochastic data by the automatic selection of a suitable order and type for a time series model of the data.