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 Hξ and the functional space L2(dFξ)

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 Hξ

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

3.3 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 Analysis of Time Series in Frequency Domain

1．Introduction

2．Principal component analysis in frequency domain and its application in AI analysis

3．Practical checking

4．Discussion

Appendix Ⅳ

Case Ⅴ．Periodicity Analysis of LH Release in Isolated Pituitary Gland by Hidden Frequency Analysis

1．Introduction

2．Statistical analysis of LH release

3．Practical rhythm analysis of LH release

4．Discussion

Case Ⅵ．Statistical Detection of Uranian Ring Signals from the Light Curve of Photoelectric Observation

1．Introduction

2．Statistical detection of weak ring signals from the noise background

3．Discussion

Case Ⅶ．On the Forecasting of Freight Transportation by a New Model Fitting Procedure of Time Series

1．Introduction

2．A new model fitting procedure for freight transportation prediction

3．Forecasting for freight transportation of practical data

4．Dicussion

Appendix Ⅶ

A.1 On the X-11 processing procedure

A.2 Simple exponential smoothing predictor

A.3 Program for fitting a spline function

Case Ⅷ．The Water Flow Prediction in Xiang River

1．Introduction

2．Constructing a prediction formula based on the hidden periodicities by the quantile method

3．Comparison and discussion

Appendix Ⅷ

A.1 Quantile method for detecting the hidden periodicities

A.2 RMA forecasting method

Case Ⅸ．Miscellaneous Cases Study

Ⅸ.1 Long term weather forecasting by seasonal ARIMA model

Ⅸ.1.1 Some relevant knowledge

(1)Seasonal ARIMA model

(2)M.L.E.and M.S.S.E.under the normal distribution

(3)Powell's algorithm for seeking the extreme value of a convex function

(4)Roots identification of a polynomial by Jury's method

Ⅸ.1.2 Modelling and forecasting for the temperature in Shanghai

Ⅸ.2 Outlier analysis and interpolation of missing data in a measuring system

Ⅸ.2.1 Basic knowledge on outlier analysis

Ⅸ.2.2 Interpolation for missing data for AR(p)model

Ⅸ.2.3 Practical application for a range measuring system

Bibliography

Subject Index