| 作者简介：Wilfredo Palma, PhD, is Chairman and Professor of Statistics in the Department of Statistics at Pontificia Universidad Católica de Chile. Dr. Palma has published several refereed articles and has received over a dozen academic honors and awards. His research interests include time series analysis, prediction theory, state space systems, linear models, and econometrics. |
| Preface Acronyms 1 Stationary Processes 1.1 Fundamental Concepts 1.1.1 Stationarity 1.1.2 Singularity and Regularity 1.1.3 Wold Decomposition Theorem 1.1.4 Causality 1.1.5 Invertibility 1.1.6 Best Linear Predictor 1.1.7 Szego-Kolmogorov Formula 1.1.8 Ergodicity 1.I.9 Martingales 1.1.10 Cumulants 1.1.11 Fractional Brownian Motion 1.1.12 Wavelets 1.2 Bibliographic Notes Problems 2 State Space Systems 2.l Introduction 2.1.1 Stability 2.1.2 Hankel Operator 2.1.3 Observability 2.1.4 Controllability 2.1.5 Minimality 2.2 Representations of Linear Processes 2.2.1 State Space Form to Wold Decomposition 2.2.2 Wold Decomposition to State Space Form 2.2.3 Hankel Operator to State Space Form 2.3 Estimation of the State 2.3.1 State Predictor 2.3.2 State Filter 2.3.3 State Smoother 2.3.4 Missing Observations 2.3.5 Steady State System 2.3.6 Prediction of Future Observations 2.4 Extensions 2.5 Bibliographic Notes Problems 3 Long-Memory Processes 3.1 Defining Long Memory 3.1.1 Alternative Definitions 3.1.2 Extensions 3.2 ARFIMA Processes 3.2.1 Stationarity, Causality, and Invertibility 3.2.2 Infinite AR and MA Expansions 3.2.3 Spectral Density 3.2.4 Autocovariance Function 3.2.5 Sample Mean 3.2.6 Partial Autocorrelations 3.2.7 Illustrations 3.2.8 Approximation of Long-Memory Processes …… 4 Estimation Methods 5 Asymptotic Theory 6 Heteroskedastic Models 7 Transformations 8 Bayesian Methods 9 Prediction 10 Regression 11 Missing Data 12 Seaonality References Topic Index Author Index |
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