György Terdik

Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis (eBook, PDF)

A Frequency Domain Approach

• Format: PDF

Produktbeschreibung

This book will be of interest to statistical researchers working in the area of time series.

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 270
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461215523
• Artikelnr.: 44052151

Autorenporträt

György Terdik received his PhD in 1982 at the Department of Probability Theory, State University of Leningrad, USSR. He has been a full-time professor at the Faculty of Informatics, University of Debrecen, Hungary since 2008. He has spent 10 semesters visiting different universities in the US including UC Berkeley and UC Santa Barbara, and the Case Western Reserve University, among others. His research interests include multivariate nonlinear statistics, time series analysis, modelling high speed communication networks, bilinear and multi-fractal models, directional statistics, and spherical processes, spatial dependence and interaction between space and time.

Inhaltsangabe

1 Foundations.- 1.1 Expectation of Nonlinear Functions of Gaussian Variables.- 1.2 Hermite Polynomials.- 1.3 Cumulants.- 1.4 Diagrams, and Moments and Cumulants for Gaussian Systems.- 1.5 Stationary processes and spectra.- 2 The Multiple Wiener-Itô Integral.- 2.1 Functions of Spaces $$ overline {L_{Phi }^{n}} $$ and $$ widetilde{{L_{Phi }^{n}}} $$.- 2.2 The multiple Wiener-Itô Integral of second order.- 2.3 The multiple Wiener-Itô integral of order n.- 2.4 Chaotic representation of stationary processes.- 3 Stationary Bilinear Models.- 3.1 Definition of bilinear models.- 3.2 Identification of a bilinear model with scalar states.- 3.3 Identification of bilinear processes, general case.- 3.4 Identification of multiple-bilinear models.- 3.5 State space realization.- 3.6 Some bilinear models of interest.- 3.7 Identification of GARCH(1,1) Model.- 4 Non-Gaussian Estimation.- 4.1 Estimating a parameter for non-Gaussian data.- 4.2 Consistency and asymptotic variance of the estimate.- 4.3 Asymptotic normality of the estimate.- 4.4 Asymptotic variance in the case of linear processes.- 5 Linearity Test.- 5.1 Quadratic predictor.- 5.2 The test statistics.- 5.3 Comments on computing the test statistics.- 5.4 Simulations and real data.- 6 Some Applications.- 6.1 Testing linearity.- 6.2 Bilinear fitting.- Appendix A Moments.- Appendix B Proofs for the Chapter Stationary Bilinear Models.- Appendix C Proofs for Section 3.6.1.- Appendix D Cumulants and Fourier Transforms for GARCH(1,1).- Appendix E Proofs for the Chapter Non-Gaussian Estimation.- E.0.1 Proof for Section 4.4.- Appendix F Proof for the Chapter Linearity Test.- References.