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E-grāmata: Analysis of Time Series: An Introduction with R

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(University of Bath, UK (Retired)),
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This new edition of this classic title, now in its seventh edition, presents a balanced and comprehensive introduction to the theory, implementation, and practice of time series analysis. The book covers a wide range of topics, including ARIMA models, forecasting methods, spectral analysis, linear systems, state-space models, the Kalman filters, nonlinear models, volatility models, and multivariate models. It also presents many examples and implementations of time series models and methods to reflect advances in the field.

Highlights of the seventh edition:

  • A new chapter on univariate volatility models

  • A revised chapter on linear time series models

  • A new section on multivariate volatility models

  • A new section on regime switching models

  • Many new worked examples, with R code integrated into the text

The book can be used as a textbook for an undergraduate or a graduate level time series course in statistics. The book does not assume many prerequisites in probability and statistics, so it is also intended for students and data analysts in engineering, economics, and finance.

Recenzijas

"Chris Chatfield has already written some popular books in statistics. Haipeng Xing is also a renowned researcher in statistics with more than 8000 citation. Efforts have been made by both authors to publish reliable data and information relating to different applications... The best part of the book is that some exercises are explained explicitly with sufficient hints. The authors also review several books on time series by other researchers from 1971 to 2010...Overall, this book is a balanced and comprehensive introduction to the theory, implementation, and practice of time series analysis in a wide range of topics. The book is intended for masters and undergraduate students in mathematics, probability, economics, statistics, astrophysics, biomedical engineering, and neuroscience. However, students who are early in a relevant PhD programme should also read this book to gain fundamental background knowledge." - Chitaranjan Mahapatra, ISCB News, July 2020

"One would never fail to notice the accessibility and the patience with which the authors introduce each of the topics in this classical textbook. The new edition successfully continues the style of the past editions, to be the one of the most accessible textbook on time series analysis. It introduces the topics with intuitions, followed with the most necessary technical details. I am particularly pleased that the R-code and data sets accompanying all the graphical analysis throughout the book, appear right where the definitions are introduced, satisfying the immediate curiosity of the readers. Together with the homework, they provide a nice platform to engage in description, explanation, prediction and control using time series data. Many data sets are updated or newly incorporated, relative to the previous version. A must-read for anyone interested in an introduction to time series." - Feng Yao, West Virginia University

Preface to the Seventh Edition xiii
Abbreviations and Notation xv
1 Introduction 1(14)
1.1 Some Representative Time Series
1(7)
1.2 Terminology
8(1)
1.3 Objectives of Time Series Analysis
9(2)
1.4 Approaches to Time Series Analysis
11(1)
1.5 Review of Books on Time Series
12(3)
2 Basic Descriptive Techniques 15(26)
2.1 Types of Variation
15(2)
2.2 Stationary Time Series
17(1)
2.3 The Time Plot
17(1)
2.4 Transformations
18(1)
2.5 Analysing Series that Contain a Trend and No Seasonal Variation
19(6)
2.5.1 Curve fitting
20(1)
2.5.2 Filtering
21(4)
2.5.3 Differencing
25(1)
2.5.4 Other approaches
25(1)
2.6 Analysing Series that Contain a Trend and Seasonal Variation
25(3)
2.7 Autocorrelation and the Correlogram
28(8)
2.7.1 The correlogram
30(1)
2.7.2 Interpreting the correlogram
31(5)
2.8 Other Tests of Randomness
36(1)
2.9 Handling Real Data
37(4)
3 Some Linear Time Series Models 41(36)
3.1 Stochastic Processes and Their Properties
41(1)
3.2 Stationary Processes
42(2)
3.3 Properties of the Autocorrelation Function
44(1)
3.4 Purely Random Processes
45(2)
3.5 Random Walks
47(1)
3.6 Moving Average Processes
47(5)
3.6.1 Stationarity and autocorrelation function of an MA process
48(1)
3.6.2 Invertibility of an MA process
49(3)
3.7 Autoregressive Processes
52(7)
3.7.1 First-order process
53(1)
3.7.2 General-order process
54(5)
3.8 Mixed ARMA Models
59(4)
3.8.1 Stationarity and invertibility conditions
60(1)
3.8.2 Yule-Walker equations and autocorrelations
60(2)
3.8.3 AR and MA representations
62(1)
3.9 Integrated ARMA (or ARIMA) Models
63(1)
3.10 Fractional Differencing and Long-Memory Models
64(5)
3.11 The General Linear Process
69(1)
3.12 Continuous Processes
69(1)
3.13 The Wold Decomposition Theorem
70(7)
4 Fitting Time Series Models in the Time Domain 77(38)
4.1 Estimating Autocovariance and Autocorrelation Functions
77(4)
4.1.1 Using the correlogram in modelling
80(1)
4.1.2 Estimating the mean
80(1)
4.1.3 Ergodicity
81(1)
4.2 Fitting an Autoregressive Process
81(7)
4.2.1 Estimating parameters of an AR process
82(2)
4.2.2 Determining the order of an AR process
84(4)
4.3 Fitting a Moving Average Process
88(6)
4.3.1 Estimating parameters of an MA process
88(2)
4.3.2 Determining the order of an MA process
90(4)
4.4 Estimating Parameters of an ARMA Model
94(3)
4.5 Model Identification Tools
97(2)
4.6 Testing for Unit Roots
99(3)
4.7 Estimating Parameters of an ARIMA Model
102(1)
4.8 Box-Jenkins Seasonal ARIMA Models
103(4)
4.9 Residual Analysis
107(3)
4.10 General Remarks on Model Building
110(5)
5 Forecasting 115(34)
5.1 Introduction
115(2)
5.2 Extrapolation and Exponential Smoothing
117(6)
5.2.1 Extrapolation of trend curves
118(1)
5.2.2 Simple exponential smoothing
118(2)
5.2.3 The Holt and Holt-Winters forecasting procedures
120(3)
5.3 The Box-Jenkins Methodology
123(12)
5.3.1 The Box-Jenkins procedures
123(4)
5.3.2 Other methods
127(1)
5.3.3 Prediction intervals
128(7)
5.4 Multivariate Procedures
135(3)
5.4.1 Multiple regression
135(2)
5.4.2 Econometric models
137(1)
5.4.3 Other multivariate models
138(1)
5.5 Comparative Review of Forecasting Procedures
138(7)
5.5.1 Forecasting competitions
139(2)
5.5.2 Choosing a non-automatic method
141(2)
5.5.3 A strategy for non-automatic univariate forecasting
143(1)
5.5.4 Summary
144(1)
5.6 Prediction Theory
145(4)
6 Stationary Processes in the Frequency Domain 149(18)
6.1 Introduction
149(1)
6.2 The Spectral Distribution Function
149(5)
6.3 The Spectral Density Function
154(3)
6.4 The Spectrum of a Continuous Process
157(1)
6.5 Derivation of Selected Spectra
158(9)
7 Spectral Analysis 167(32)
7.1 Fourier Analysis
167(1)
7.2 A Simple Sinusoidal Model
168(4)
7.3 Periodogram Analysis
172(5)
7.3.1 The relationship between the periodogram and the autocovariance function
175(1)
7.3.2 Properties of the periodogram
175(2)
7.4 Some Consistent Estimation Procedures
177(8)
7.4.1 Transforming the truncated autocovariance function
177(2)
7.4.2 Hanning
179(1)
7.4.3 Hamming
180(1)
7.4.4 Smoothing the periodogram
180(3)
7.4.5 The fast Fourier transform (FFT)
183(2)
7.5 Confidence Intervals for the Spectrum
185(1)
7.6 Comparison of Different Estimation Procedures
186(5)
7.7 Analysing a Continuous Time Series
191(2)
7.8 Examples and Discussion
193(6)
8 Bivariate Processes 199(18)
8.1 Cross-Covariance and Cross-Correlation
199(5)
8.1.1 Examples
201(1)
8.1.2 Estimation
202(1)
8.1.3 Interpretation
203(1)
8.2 The Cross-Spectrum
204(13)
8.2.1 Examples
206(3)
8.2.2 Estimation
209(2)
8.2.3 Interpretation
211(6)
9 Linear Systems 217(36)
9.1 Introduction
217(2)
9.2 Linear Systems in the Time Domain
219(4)
9.2.1 Some types of linear systems
219(2)
9.2.2 The impulse response function: An explanation
221(1)
9.2.3 The step response function
222(1)
9.3 Linear Systems in the Frequency Domain
223(15)
9.3.1 The frequency response function
223(4)
9.3.2 Gain and phase diagrams
227(2)
9.3.3 Some examples
229(2)
9.3.4 General relation between input and output
231(5)
9.3.5 Linear systems in series
236(1)
9.3.6 Design of filters
237(1)
9.4 Identification of Linear Systems
238(15)
9.4.1 Estimating the frequency response function
240(3)
9.4.2 The Box-Jenkins approach
243(4)
9.4.3 Systems involving feedback
247(6)
10 State-Space Models and the Kalman Filter 253(14)
10.1 State-Space Models
253(8)
10.1.1 The random walk plus noise model
256(1)
10.1.2 The linear growth model
256(1)
10.1.3 The basic structural model
257(1)
10.1.4 State-space representation of an AR(2) process
258(1)
10.1.5 Bayesian forecasting
259(1)
10.1.6 A regression model with time-varying coefficients
260(1)
10.1.7 Model building
260(1)
10.2 The Kalman Filter
261(6)
11 Non-Linear Models 267(36)
11.1 Introduction
267(6)
11.1.1 Why non-linearity?
267(3)
11.1.2 What is a linear model?
270(1)
11.1.3 What is a non-linear model?
271(1)
11.1.4 What is white noise?
272(1)
11.2 Non-Linear Autoregressive Processes
273(1)
11.3 Threshold Autoregressive Models
274(6)
11.4 Smooth Transition Autoregressive Models
280(4)
11.5 Bilinear Models
284(1)
11.6 Regime-Switching Models
285(5)
11.7 Neural Networks
290(6)
11.8 Chaos
296(4)
11.9 Concluding Remarks
300(1)
11.10 Bibliography
301(2)
12 Volatility Models 303(20)
12.1 Structure of a Model for Asset Returns
303(2)
12.2 Historic Volatility
305(1)
12.3 Autoregressive Conditional Heteroskedastic (ARCH) Models
306(5)
12.4 Generalized ARCH Models
311(4)
12.5 The ARMA-GARCH Models
315(3)
12.6 Other ARCH-Type Models
318(2)
12.6.1 The integrated GARCH model
319(1)
12.6.2 The exponential GARCH model
320(1)
12.7 Stochastic Volatility Models
320(1)
12.8 Bibliography
321(2)
13 Multivariate Time Series Modelling 323(28)
13.1 Introduction
323(7)
13.1.1 One equation or many?
324(2)
13.1.2 The cross-correlation function
326(1)
13.1.3 Initial data analysis
327(3)
13.2 Single Equation Models
330(1)
13.3 Vector Autoregressive Models
331(3)
13.3.1 VAR(1) models
331(1)
13.3.2 VAR(p) models
332(2)
13.4 Vector ARMA Models
334(1)
13.5 Fitting VAR and VARMA Models
335(9)
13.6 Co-Integration
344(1)
13.7 Multivariate Volatility Models
345(3)
13.7.1 Exponentially weighted estimate
345(1)
13.7.2 BEKK models
346(2)
13.8 Bibliography
348(3)
14 Some More Advanced Topics 351(14)
14.1 Modelling Non-Stationary Time Series
351(2)
14.2 Model Uncertainty
353(2)
14.3 Control Theory
355(1)
14.4 Miscellanea
356(9)
14.4.1 Autoregressive spectrum estimation
357(1)
14.4.2 Wavelets
357(1)
14.4.3 'Crossing' problems
358(1)
14.4.4 Observations at unequal intervals, including missing values
358(1)
14.4.5 Outliers and robust methods
359(2)
14.4.6 Repeated measurements
361(1)
14.4.7 Aggregation of time series
361(1)
14.4.8 Spatial and spatio-temporal series
362(1)
14.4.9 Time series in finance
362(2)
14.4.10 Discrete-valued time series
364(1)
Appendix A Fourier, Laplace, and z-Transforms 365(4)
Appendix B Dirac Delta Function 369(2)
Appendix C Covariance and Correlation 371(2)
Answers to Exercises 373(8)
References 381(14)
Index 395
Chris Chatfield is a retired Reader in Statistics at the University of Bath, UK, the author of five books and numerous research papers, and an elected Honorary Fellow of the International Institute of Forecasters.

Haipeng Xing is an associate professor in Applied Mathematics and Statistics at the State University of New York, Stony Brook, USA, the author of two books and numerous research papers. His research interests include quantitative finance and risk management, econometrics, applied stochastic control, and sequential statistical methodology.
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