2010年5月时间序列新书 introduction to time series modeling

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Price:  $79.95
Cat. #:  C9217
ISBN:  9781584889212
ISBN 10:  1584889217
Publication Date:  April 21, 2010
Number of Pages:  296
Availability:  In Stock
Binding(s):  Hardback
Features

• Presents a model-based method of analyzing, predicting, and simulating time series with various characteristics
• Uses real data sets from economics, finance, seismology, meteorology, and ship engineering
• Extends the state-space approach to more general nonlinear or non-Gaussian state-space models
• Includes methods and models developed by the author and his colleagues at the Institute of Statistical Mathematics

Summary
In time series modeling, the behavior of a certain phenomenon is expressed in relation to the past values of itself and other covariates. Since many important phenomena in statistical analysis are actually time series and the identification of conditional distribution of the phenomenon is an essential part of the statistical modeling, it is very important and useful to learn fundamental methods of time series modeling. Illustrating how to build models for time series using basic methods, Introduction to Time Series Modeling covers numerous time series models and the various tools for handling them.

The book employs the state-space model as a generic tool for time series modeling and presents convenient recursive filtering and smoothing methods, including the Kalman filter, the non-Gaussian filter, and the sequential Monte Carlo filter, for the state-space models. Taking a unified approach to model evaluation based on the entropy maximization principle advocated by Dr. Akaike, the author derives various methods of parameter estimation, such as the least squares method, the maximum likelihood method, recursive estimation for state-space models, and model selection by the Akaike information criterion (AIC). Along with simulation methods, he also covers standard stationary time series models, such as AR and ARMA models, as well as nonstationary time series models, including the locally stationary AR model, the trend model, the seasonal adjustment model, and the time-varying coefficient AR model.

With a focus on the description, modeling, prediction, and signal extraction of times series, this book provides basic tools for analyzing time series that arise in real-world problems. It encourages readers to build models for their own real-life problems.

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关键词：introduction Time Series troduction Modeling Series interested finance method

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作者：Genshiro Kitagawa
出版社：Chapman and Hall/CRC
目录：
1 Introduction and Preparatory Analysis 1
1.1 Time Series Data 1
1.2 Classification of Time Series 6
1.3 Objectives of Time Series Analysis 8
1.4 Pre-processing of Time Series 8
1.4.1 Transformation of variables 9
1.4.2 Differencing 9
1.4.3 Change from the previous month (quarter) and
annual change 10
1.4.4 Moving average 11
1.5 Organization of This Book 13
2 The Covariance Function 17
2.1 The Distribution of Time Series and Stationarity 17
2.2 The Autocovariance Function of Stationary Time Series 20
2.3 Estimation of the Autocovariance Function 21
2.4 Multivariate Time Series and Scatterplots 24
2.5 Cross-Covariance Function and Cross-Correlation
Function 26
3 The Power Spectrum and the Periodogram 31
3.1 The Power Spectrum 31
3.2 The Periodogram 36
3.3 Averaging and Smoothing of the Periodogram 40
3.4 Computational Method of Periodogram 44
3.5 Computation of the Periodogram by Fast Fourier Transform
44
4 StatisticalModeling 49
4.1 Probability Distributions and Statistical Models 49
4.2 K-L Information and the Entropy Maximization Principle
54
4.3 Estimation of the K-L Information and Log-Likelihood 56
4.4 Estimation of Parameters by the Maximum Likelihood
Method 58
4.5 AIC (Akaike Information Criterion) 62
4.5.1 Evaluation of C1 64
4.5.2 Evaluation of C3 65
4.5.3 Evaluation of C2 66
4.5.4 Evaluation of C and AIC 66
4.6 Transformation of Data 66
5 The Least Squares Method 71
5.1 Regression Models and the Least Squares Method 71
5.2 Householder Transformation 73
5.3 Selection of Order by AIC 75
5.4 Addition of Data and Successive HouseholderReduction 78
5.5 Variable Selection by AIC 79
6 Analysis of Time Series Using ARMA Models 83
6.1 ARMA Model 83
6.2 The Impulse Response Function 84
6.3 The Autocovariance Function 85
6.4 The Relation Between AR Coefficients and the PARCOR
88
6.5 The Power Spectrum of the ARMA Process 88
6.6 The Characteristic Equation 92
6.7 The Multivariate AR Model 93
7 Estimation of an AR Model 103
7.1 Fitting an AR Model 103
7.2 Yule-Walker Method and Levinson’s Algorithm 105
7.3 Estimation of an AR Model by the Least Squares
Method 106
7.4 Estimation of an AR Model by the PARCOR Method 108
7.5 Large Sample Distribution of the Estimates 111
7.6 Estimation of a Multivariate AR Model by the Yule-
Walker Method 113
7.7 Estimation of a Multivariate AR Model by the Least
Squares Method 117
8 The Locally Stationary AR Model 123
8.1 Locally Stationary AR Model 123
8.2 Automatic Partitioning of the Time Interval into an
Arbitrary Number of Subintervals 125
8.3 Precise Estimation of a Change Point 130
9 Analysis of Time Series with a State-SpaceModel 135
9.1 The State-Space Model 135
9.2 State Estimation via the Kalman Filter 138
9.3 Smoothing Algorithms 140
9.4 Increasing Horizon Prediction of the State 140
9.5 Prediction of Time Series 141
9.6 Likelihood Computation and Parameter Estimation for a
Time Series Model 144
9.7 Interpolation of Missing Observations 147
10 Estimation of the ARMA Model 151
10.1 State-Space Representation of the ARMA Model 151
10.2 Initial State of an ARMA Model 152
10.3 Maximum Likelihood Estimate of an ARMA Model 153
10.4 Initial Estimates of Parameters 154
11 Estimation of Trends 159
11.1 The Polynomial Trend Model 159
11.2 Trend Component Model–Model for Probabilistic
Structural Changes 162
11.3 Trend Model 165
12 The Seasonal Adjustment Model 173
12.1 Seasonal ComponentModel 173
12.2 Standard Seasonal Adjustment Model 176
12.3 Decomposition Including an AR Component 179
12.4 Decomposition Including a Trading-Day Effect 184
13 Time-Varying Coefficient AR Model 189
13.1 Time-Varying Variance Model 189
13.2 Time-Varying Coefficient AR Model 192
13.3 Estimation of the Time-Varying Spectrum 197
13.4 The Assumption on System Noise for the Time-Varying
Coefficient AR Model 198
13.5 Abrupt Changes of Coefficients 199
14 Non-Gaussian State-SpaceModel 203
14.1 Necessity of Non-Gaussian Models 203
14.2 Non-Gaussian State-Space Models and State Estimation 204
14.3 Numerical Computation of the State Estimation Formula 206
14.4 Non-Gaussian Trend Model 209
14.5 A Time-Varying Variance Model 213
14.6 Applications of Non-Gaussian State-Space Model 217
14.6.1 Processing of the outliers by a mixture of
Gaussian distributions 217
14.6.2 A nonstationary discrete process 218
14.6.3 A direct method of estimating the time-varying
variance 219
15 The Sequential Monte Carlo Filter 221
15.1 The Nonlinear Non-Gaussian State-Space Model and
Approximations of Distributions 221
15.2 Monte Carlo Filter 225
15.2.1 One-step-ahead prediction 225
15.2.2 Filtering 225
15.2.3 Algorithm for the Monte Carlo filter 226
15.2.4 Likelihood of a model 226
15.2.5 Re-sampling method 227
15.2.6 Numerical examples 228
15.3 Monte Carlo Smoothing Method 231
15.4 Nonlinear Smoothing 233
16 Simulation 237
16.1 Generation of Uniform Random Numbers 237
16.2 Generation of Gaussian White Noise 239
16.3 Simulation Using a State-Space Model 241
16.4 Simulation with Non-Gaussian Model 243
16.4.1 c2 distribution 244
16.4.2 Cauchy distribution 244
16.4.3 Arbitrary distribution 244
A Algorithms for Nonlinear Optimization 249
B Derivation of Levinson’s Algorithm 251
C Derivation of the Kalman Filter
and Smoother Algorithms 255
C.1 Kalman Filter 255
C.2 Smoothing 256
D Algorithm for the Monte Carlo Filter 259
D.1 One-Step-Ahead Prediction 259
D.2 Filter 260
D.3 Smoothing 261
Answers to the Problems 263
Bibliography 277
Index 285

太好了，最新版的，呵呵，可是没币啊

好像只讨论了线性时间序列呀