Preface
PART ONE
An Introduction to the Theory and Methods of Time Series Analysis
Chapter 1.Theory of Stationary Time Series
1.1 The definition of stationary stochastic processes
1.2 The spectral representation of covariance function
1.3 The Hilbert space of second order processes
1.4 Stochastic integral and the isomorphic relationship between H~ and the functional space L2(dFe)
1.4.1 Orthogonal stochastic measure
1.4.2 Stochastic integral and the representation of stationary processes
1.4.3.Karhunen theorem
1.5 Strong law of large numbers for stationary series
1.6 Sampling theorem for stochastic stationary processes
Chapter 2.ARMA Model and Model Fitting
2.1 ARMA model and the Wold decomposition
2.2 Orthogonal basis in Hilbert space Hf
2.3 The covariance function of ARMA model and Yule-Walker equation
2.4 Model fitting under the criterion of one-step ahead prediction error
2.5 M.E.model fitting for observed data
2.5.1 M.E.model fitting with sample covariance
2.5.2 Order selection problem
Chapter 3.Prediction, Filtering and Spectral Analysis of Time Series
3.1 Prediction of time series
3.1.1 The prediction formula for AR models
3.1.2 The prediction formula for ARMA models
3.2 The linear filtering of time series
a.a Spectral analysis of time series
3.3.1 Theory and methods of hidden periodicities analysis
3.3.2 Theory and methods of spectral density estimations
PART TWO Case Studies in Time Series Analysis
Case I.Digital Processing of a Dynamic Marine Gravity Meter
1.Problem statement and working diagram of a dynamic marine gravity meter
2.The first test for solving the problem
3.Design a new digital filter under Min-Max criterion
4.The frequency rectification by filtering
5.Practical checking in the prospecting field of the East Sea of China
Case II.Digital Filters Design by Maximum Entropy Modelling
1.Problem statement
2.Design the filter by maximum entropy modelling
3.A practical filter design
Case III.The Spectral Analysis of the Visual Evoked Potentials of Normal and Congenital Dull Children (Down's disease)
1.Introduction
2.Spectral analysis of VEP records for dull and normal children
3.Statistical analysis for detection of characteristics
4.Physiological interpretation
Appendix III
Case IV.Statistical Analysis of VEP and AI by the Principal Component Analyis of Time Serise in Frequency Domain
Case V.Periodicity Analysis of LH Release in Isolated Pituitary Gland by Hidden Frequency Analysis
Case VI.Statistical Detection of Uranian Ring Signnals from the Light Curve of Photoelectric Observation
Case VII.On the Forecasting of Freight Transportation by a New Model Fitting Procedure of Time Series
Case VIII.The Water Flow Prediction in Xiang River
Case IX.Miscellaneous Cases Study
Bibliography
Subject Index
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