Time Series Analysis And Its Applications

by Shumway, Robert H.; Stoffer, David S.

• ISBN13: 9780387293172
• ISBN10: 0387293175
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-06-30
• Publisher: Springer Verlag

Summary

Time Series Analysis and Its Applications presents a balanced and comprehensive treatment of both time and frequency domain methods with accompanying theory. Numerous examples using non-trivial data illustrate solutions to problems such as evaluating pain perception experiments using magnetic resonance imaging or monitoring a nuclear test ban treaty. The book is designed to be useful as a text for graduate level students in the physical, biological and social sciences and as a graduate level text in statistics. Some parts may also serve as an undergraduate introductory course.Theory and methodology are separated to allow presentations on different levels. Material from the earlier 1988 Prentice-Hall text Applied Statistical Time Series Analysis has been updated by adding modern developments involving categorical time sries analysis and the spectral envelope, multivariate spectral methods, long memory series, nonlinear models, longitudinal data analysis, resampling techniques, ARCH models, stochastic volatility, wavelets and Monte Carlo Markov chain integration methods. These add to a classical coverage of time series regression, univariate and multivariate ARIMA models, spectral analysis and state-space models. The book is complemented by ofering accessibility, via the World Wide Web, to the data and an exploratory time series analysis program ASTSA for Windows that can be downloaded as Freeware.Robert H. Shumway is Professor of Statistics at the University of California, Davis. He is a Fellow of the American Statistical Association and a member of the Inernational Statistical Institute. He won the 1986 American Statistical Association Award for Outstanding Statistical Application and the 1992 Communicable Diseases Center Statistics Award; both awards were for joint papers on time series applications. He is the author of a previous 1988 Prentice-Hall text on applied time series analysis and is currenlty a Departmental Editor for the Journal of Forecasting.David S. Stoffer is Professor of Statistics at the University of Pittsburgh. He has made seminal contributions to the analysis of categorical time series and won the 1989 American Statistical Association Award for Outstanding Statistical Application in a joint paper analyzing categorical time series arising in infant sleep-state cycling. He is currently an Associate Editor of the Journal of Forecasting and has served as an Associate Editor for the Journal fo the American Statistical Association.

Table of Contents

1 Characteristics of Time Series	1	(47)
1.1 Introduction	1	(3)
1.2 The Nature of Time Series Data	4	(7)
1.3 Time Series Statistical Models	11	(7)
1.4 Measures of Dependence: Autocorrelation and Cross-Correlation	18	(5)
1.5 Stationary Time Series	23	(6)
1.6 Estimation of Correlation	29	(5)
1.7 Vector-Valued and Multidimensional Series	34	(6)
Problems	40	(8)
2 Time Series Regression and Exploratory Data Analysis	48	(36)
2.1 Introduction	48	(1)
2.2 Classical Regression in the Time Series Context	49	(8)
2.3 Exploratory Data Analysis	57	(14)
2.4 Smoothing in the Time Series Context	71	(8)
Problems	79	(5)
3 ARIMA Models	84	(90)
3.1 Introduction	84	(1)
3.2 Autoregressive Moving Average Models	85	(13)
3.3 Difference Equations	98	(5)
3.4 Autocorrelation and Partial Autocorrelation Functions	103	(7)
3.5 Forecasting	110	(12)
3.6 Estimation	122	(18)
3.7 Integrated Models for Nonstationary Data	140	(3)
3.8 Building ARIMA Models	143	(11)
3.9 Multiplicative Seasonal ARIMA Models	154	(11)
Problems	165	(9)
4 Spectral Analysis and Filtering	174	(97)
4.1 Introduction	174	(2)
4.2 Cyclical Behavior and Periodicity	176	(5)
4.3 The Spectral Density	181	(6)
4.4 Periodogram and Discrete Fourier Transform	187	(10)
4.5 Nonparametric Spectral Estimation	197	(18)
4.6 Multiple Series and Cross-Spectra	215	(5)
4.7 Linear Filters	220	(8)
4.8 Parametric Spectral Estimation	228	(4)
4.9 Dynamic Fourier Analysis and Wavelets	232	(13)
4.10 Lagged Regression Models	245	(6)
4.11 Signal Extraction and Optimum Filtering	251	(5)
4.12 Spectral Analysis of Multidimensional Series	256	(2)
Problems	258	(13)
5 Additional Time Domain Topics	271	(53)
5.1 Introduction	271	(1)
5.2 Long Memory ARMA and Fractional Differencing	271	(9)
5.3 GARCH Models	280	(9)
5.4 Threshold Models	289	(4)
5.5 Regression with Autocorrelated Errors	293	(2)
5.6 Lagged Regression: Transfer Function Modeling	295	(7)
5.7 Multivariate ARMAX Models	302	(18)
Problems	320	(4)
6 State-Space Models	324	(88)
6.1 Introduction	324	(6)
6.2 Filtering, Smoothing, and Forecasting	330	(9)
6.3 Maximum Likelihood Estimation	339	(9)
6.4 Missing Data Modifications	348	(4)
6.5 Structural Models: Signal Extraction and Forecasting	352	(3)
6.6 ARMAX Models in State-Space Form	355	(2)
6.7 Bootstrapping State-Space Models	357	(5)
6.8 Dynamic Linear Models with Switching	362	(14)
6.9 Nonlinear and Non-nornial State-Space Models Using Moute Carlo Methods	376	(6)
6.10 Stochastic Volatility	382	(12)
6.11 State-Space and ARMAX Models for Longitudinal Data Analysis	394	(10)
Problems	404	(8)
7 Statistical Methods in the Frequency Domain	412	(89)
7.1 Introdnction	412	(4)
7.2 Spectral Matrices and Likelihood Functions	416	(1)
7.3 Regression for Jointly Stationary Series	417	(9)
7.4 Regression with Deterministic Inputs	426	(8)
7.5 Random Coefficient Regression	434	(4)
7.6 Analysis of Designed Experiments	438	(11)
7.7 Discrimination and Cluster Analysis	449	(15)
7.8 Principal Components and Factor Analysis	464	(15)
7.9 The Spectral Envelope	479	(16)
Problems	495	(6)
Appendix A: Large Sample Theory	501	(21)
A.1 Convergence Modes	501	(8)
A.2 Central Limit Theorems	509	(4)
A.3 The Mean and Autocorrelation Functions	513	(9)
Appendix B: Time Domain Theory	522	(12)
B.1 Hilbert Spaces and the Projection Theorem	522	(4)
B.2 Causal Conditions for ARMA Models	526	(2)
B.3 Large Sample Distribution of the AR(p) Conditional Least Squares Estimators	528	(4)
B.4 The Wold Decomposition	532	(2)
Appendix C: Spectral Domain Theory	534	(21)
C.1 Spectral Representation Theorem	534	(5)
C.2 Large Sample Distribution of the DFT and Smoothed Periodogram	539	(11)
C.3 The Complex Multivariate Normal Distribution	550	(5)
References	555	(14)
Index	569