Periodically correlated random sequences : spectral theory and practice

摘要: Preface. Acknowledgments. Glossary. 1. Introduction. 1.1 Summary. 1.2 Historical Notes. Problems. 2. Examples, Models and Simulations. 2.1 Examples Models. 2.1.1 Random Periodic Sequences. 2.1.2 Sums of Stationary 2.1.3 Products Scalar 2.1.4 Time Scale Modulation 2.1.5 Pulse Amplitude Modulation. 2.1.6 A More General Example. 2.1.7 Autoregressive 2.1.8 Moving Average 2.1.9 Periodically Perturbed Dynamical Systems. 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.2.5 Logistic Maps. 2.2.6 2.2.7 3. Review Hilbert Spaces. 3.1 Vector 3.2 Inner Product 3.3 3.4 Operators. 3.5 Projection 3.6 Spectral Theory Unitary 3.6.1 Measures. 3.6.2 Integrals. 3.6.3 Theorems. 4. 4.1 Univariate Theory. 4.1.1 Shift. 4.1.2 Representation. 4.1.3 Mean Ergodic Theorem. 4.1.4 Domain. 4.2 Prediction 4.2.1 Infinite Past, Regularity Singularity. 4.2.2 Wold Decomposition. 4.2.3 Innovation Subspaces. 4.2.4 Prediction. 4.2.5 Finite Past 4.3 Multivariate 4.3.1 4.3.2 4.3.3 4.3.4 4.4 4.4.1 4.4.2 4.4.3 Innovations Rank. 4.4.4 Regular Processes. 4.4.5 4.4.6 4.4.7 4.4.8 5. Harmonizable 5.1 Measure Integration. 5.2 5.3 Limit Average. 5.4 Linear Invariant Filters. 6. Fourier the Covariance. 6.1 Series Representation 6.2 Harmonizability R(s t). 6.2.1 Xt. 6.4 Covariance Spectra for Specific Cases. 6.4.1 PC White Noise. 6.4.2 6.5 Asymptotic Stationarity. 6.6 Lebesgue Decomposition F. 6.7 The spectrum mt. 6.8 Effects Common Operations on 6.8.1 Filtering. 6.8.2 Differencing. 6.8.3 Shifts. 6.8.4 Sampling. 6.8.5 Bandshifting. 6.8.6 Varying (PTV) 7. Representations 7.1 Operator a Sequence. 7.2 Based Operator. 7.2.1 Gladyshev 7.2.2 Another Type. 7.2.3 Time-dependent 7.2.4 Again. 7.2.5 Principal Components. 7.3 7.4 Sequences as Projections 8. 8.1 8.2 Innovations. 8.3 Autoregressions Order 8.4 Density 8.4.1 Densities PAR(1). 8.5 Least Square 8.5.1 Past. 8.5.2 PAR(1) 8.5.3 9. Estimation 9.1 mt : 9.2 Practice. 10. Estimation. 10.1 Shifted Periodogram. 10.2 Consistent Estimators. 10.3 Normality. 10.4 Coherence 363. 10.4.1 Known T. 10.4.2 Unknown 10.5 10.5.1 Confidence Intervals. 10.5.2 Examples. 10.6 Discrete 10.6.1 Removal Mean. 10.6.2 Testing Additive 10.6.3 Detected 11. Paradigm Nonparametric Analysis Series. 11.1 Period T is Known. 11.2 Unknown. References. Index.