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Time Series Forecasting, Simulation, Applications(1993)
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Janacek/Swift
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E-H
ISBN
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0139184597
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720 Point
Preface
1. Introduction
1.1. Smoothing and seasonal adjustment
1.2. Regression methods
1.3. The backward difference operator
1.4. Forecasting and moving averages
2. Stationarity
2.3. Generating Gaussian series
2.4. Stationarity and prediction and non-deterministic series
2.5. The general linear representation
2.6. Prediction
2.7. Sample estimates
3. Time series models
3.2. Three simple models
3.3. Estimation
3.4. Forecasting
3.5. Model evaluation
3.6. Model selection
3.7. Identification
3.8. Exponential smoothing and all that
3.9. Simulation
Appendix: A random number generator
4. The general state space model
4.2. Properties of state space models
4.3. Identification
4.4. Evaluating the likelihood function
4.5. Maximizing the likelihood function
4.6. Prediction
4.7. Model selection, comparison and evaluation
4.8. Simulation of state space models
5. ARMA (Box-Jenkins) models
5.2. Stationarity
5.3. Invertibility and identification
5.4. Properties of stationary ARMA models
5.5. Estimation
5.6. Non-stationary models
5.7. Model selection
5.8. Forecasting ARMA models
5.9. Model evaluation
5.10. Seasonal ARMA models
5.11. Exponential smoothing and ARMA models
5.12. Simulation of ARMA models
Appendix 5.1: On linear difference equations
Appendix 5.2: The Durbin-Levinson recursion
6. Structural state space models
6.2. Some further structural models
6.3. Properties of structural models
6.4. Estimation
6.5. Diagnostic checking and prediction
6.6. Model selection
6.7. Connections: ARMA models, structural models, and exponential smoothing
6.8. Bayesian time series models
6.9. Structural models - parts of the analyst's toolkit
7. The frequency domain
7.2. Some definitions
7.3. Cycles, waves, and Fourier analysis
7.4. Discrete and continuous series: aliasing
7.5. Fourier analysis - the Fourier series
7.6. The discrete Fourier transform (DFT)
7.7. The z transform
7.8. The fast Fourier transform (FFT)
7.9. A heuristic spectrum
Appendix 7.1: Fourier transforms
8. The spectrum
8.3. Examples of spectra
8.4. The spectral representation
8.5. Linear filters
8.6. Filter design
8.7. Forecasting
8.8. Sampling and aliasing
8.9. Transformations and the combination of series
9. Estimation in the frequency domain
9.1. The periodogram
9.2. Applications of the periodogram
9.3. Estimating the spectrum: non-parametric estimates
9.4. Lag windows
9.5. Sampling properties of the smoothed spectral estimate
9.6. Some examples
9.7. Parametric spectral estimates
9.8. Estimation in the frequency domain
10. Odds and ends: a taste of some more advanced topics
10.2. Transformations
10.3. Coping with missing values
10.4. Incorporating explanatory variables in the time series model
10.5. Modelling more than one time series model
10.6. Multiple series: the frequency domain
10.7. Non-linear and non-standard models
References
Data appendix
Index
"I reviewed this book for the American Statistician in 1994. The book provides extensive coverage of time series methodology without being overly theoretical. The authors are well versed on the topic as they have published on it in the statistical literature. They avoid delving into the difficult theory by sketching out the mathematics, present the key theorems and refer the reader to other sources for rigorous details. They provide a broad treatment of both the time and frequency domain approaches to time series analysis. It is at the level of an advanced undergraduate or beginning graduate level course. Still there is more coverage of the time domain.
Traditional time domain models including exponential smoothing and moving averages are introduced first. The ARMA models and Harvey's structural models are treated as special cases of the state space models. They introduce many parameter estimation procedures but make the key point that many of them are simply useful approximations to the maximum likelihood estimates. They discuss applications with reference to the software packages MINITAB and SYSTAT (now owned by SPSS Inc.).
My criticism of it is with regard to omissions. They talk about the NAG libraries but neglect IMSL. The routines in SPlus that were available at the time of publication of the book were also overlooked. They also overlooked the recent advances on detecting outliers in time series as was covered in the 1984 2nd edition of "Outliers in Statistical Data" by Barnett and Lewis. Further work can now be found in the 3rd edition of the Barnett and Lewis book that came out in 1995. Although forecasting (or prediction) is perhaps the most important application of time series methodology, it is also worthwhile in a book like this intended for engineers and other practitioners that other applications be discussed. Discrimination is one such topic. Certain time series (e.g. radar signals) must be detected and discriminated from noise and then further identified by type. In biomedical applications a patient's electroencephalogram or electrocardiagram are routinely studied to look for abnormalities that could indicate neurological or heart diseases respectively. Shumway covers this well in his book "Applied Statistical Time Series" published in 1988 and more examples can be found in his 2000 book "Time Series and Its Applications" coauthored with David Stoffer. There they look at the interesting problem of discriminating between earthquake activity and nuclear explosions. New methods involving wavelet transforms are now used. This is discussed in the Shumway and Stoffer book and in detail in the new book on Wavelets by Percival and Walden.
Chapters 6-12 are somewhat lacking in exercises while chapters 1-5 provide enough exercises for class homework. A course based on this text would benefit from additional exercises and some case studies provided by the instructor. Also new material developed in the last 8 years should be covered in such a course.
Some mention of Bayesian methods is given in chapter 6 with particular reference to the book by West and Harrison. Additional developments have been published in the last 8 years including additional articles and books by Mike West and his coauthors."
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