Author | Terdik, Gyรถrgy. author |
---|---|
Title | Bilinear Stochastic Models and Related Problems of Nonlinear Time Series Analysis [electronic resource] : A Frequency Domain Approach / by Gyรถrgy Terdik |
Imprint | New York, NY : Springer New York : Imprint: Springer, 1999 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1552-3 |
Descript | XV, 270 p. 25 illus. online resource |
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-Itรด Integral -- 2.1 Functions of Spaces $$ \overline {L_{\Phi }̂{n}} $$ and $$ \widetilde{{L_{\Phi }̂{n}}} $$ -- 2.2 The multiple Wiener-Itรด Integral of second order -- 2.3 The multiple Wiener-Itรด 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