Multiple time series [[electronic resource] /] / E. J. Hannan

• Record Nr.: UNINA9910144694603321
• Autore: Hannan E. J (Edward James), <1921->
• Pubbl/distr/stampa: New York, : Wiley, 1970
• ISBN: 1-282-30760-6; 9786612307607; 0-470-31642-X; 0-470-31713-2
• Descrizione fisica: 1 online resource (552 p.)
• Collana: Wiley series in probability and mathematical statistics
• Disciplina: 519.232; 519.8
• Soggetti: Mathematical statistics; Time-series analysis
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliography: p. 519-527.
• Nota di contenuto: Multiple Time Series; Contents; PART I. BASIC THEORY; CHAPTER I. INTRODUCTORY THEORY; 1. Introduction; 2. Differentiation and Integration of Stochastic Processes; 3. Some Special Models; 4. Stationary Processes and their Covariance Structure; 5. Higher Moments; 6. Generalized Random Processes; EXERCISES; APPENDIX; CHAPTER II. THE SPECTRAL THEORY OF VECTOR PROCESSES; 1. Introduction; 2. The Spectral Theorems for Continuous-Time Stationary Processes; 3. Sampling a Continuous-Time Process. Discrete Time Processes; 4. Linear Filters; 5 . Some Special Models; 6. Some Spectral Theory for Nonstationary Processes7. Nonlinear Transformations of Random Processes; 8. Higher Order Spectra; 9. Spectral Theory for GRP; 10. Spectral Theories for Homogeneous Random Processes on Other Spaces; 11. Filters, General Theory; EXERCISES; APPENDIX; CHAPTER III. PREDICTION THEORY AND SMOOTHING; 1. Introduction; 2. Vector Discrete-Time Prediction for Rational Spectra; 3. The General Theory for Stationary, Discrete-Time, Scalar Processes; 4. The General Theory for Stationary, Continuous-Time, Scalar Processes; 5. Vector Discrete-Time Prediction; 6. Problems of Interpolation7. Smoothing and Signal Measurement; 8. ; Kalman Filtering; 9. Smoothing Filters; EXERCISES; PART II. INFERENCE; CHAPTER IV. THE LAWS OF LARGE NUMBERS AND THE CENTRAL LIMIT THEOREM; 1. Introduction; 2. Strictly Stationary Processes. Ergodic Theory; 3. Second-Order Stationary Processes. Ergodic Theory; 4. The Central Limit Theorem; EXERCISES; APPENDIX; CHAPTER V. INFERENCE ABOUT SPECTRA; 1. Introduction; 2. The Finite Fourier Transform; 3. Alternative Computational Procedures for the FFT; 4. Estimates of Spectral for large Nand N/M; 5. The Asymptotic Distribution of Spectral Estimates6. Complex Multivariate Analysis; EXERCISES; APPENDIX; CHAPTER VI. INFERENCE FOR RATIONAL SPECTRA; 1. Introduction; 2. Inference for Autoregressive Models. Asymptotic Theory; 3. Inference for Autoregressive Models. Some Exact Theory; 4. Moving Average and Mixed Autoregressive, Moving Average Models. Introduction; 5. The Estimation of Moving Average and Mixed Moving Average Autoregressive Models Using Spectral Methods; 6. General Theories of Estimation for Finite Parameter Models; 7. Tests of Goodness of Fit; 8. Continuous-Time Processes and Discrete ApproximationsEXERCISES; APPENDIX; CHAPTER VII. REGRESSION METHODS; 1. Introduction; 2. The Efficiency of Least Squares. Fixed Sample Size; 3. The Efficiency of Least Squares. Asymptotic Theory; 4. The Efficient Estimation of Regressions; 5. The Effects of Regression Procedures on Analysis of Residuals; 6. Tests for Periodicities; 7. Distributed Lag Relationships; EXERCISES; APPENDIX; MATHEMATICAL APPENDIX; BIBLIOGRAPHY; TABLE OF NOTATIONS; INDEX