György Terdik

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

A Frequency Domain Approach

• Format: PDF

Produktbeschreibung

The object of the present work is a systematic statistical analysis of bilinear processes in the frequency domain. The first two chapters are devoted to the basic theory of nonlinear functions of stationary Gaussian processes, Hermite polynomials, cumulants and higher order spectra, multiple Wiener-Itô integrals and finally chaotic Wiener-Itô spectral representation of subordinated processes. There are two chapters for general nonlinear time series problems.

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Produktdetails

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

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.