- Hardcover: 820 pages
- Publisher: Princeton University Press; 1 edition (January 11, 1994)
- Language: English
- ISBN-10: 0691042896
- ISBN-13: 978-0691042893
- Product Dimensions: 7 x 2.2 x 10.1 inches
- Shipping Weight: 3.6 pounds (View shipping rates and policies)
- Average Customer Review: 4.5 out of 5 stars See all reviews (46 customer reviews)
- Amazon Best Sellers Rank: #70,990 in Books (See Top 100 in Books)
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Time Series Analysis 1st Edition
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"A carefully prepared and well written book. . . . Without doubt, it can be recommended as a very valuable encyclopedia and textbook for a reader who is looking for a mainly theoretical textbook which combines traditional time series analysis with a review of recent research areas."--Journal of Economics
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"I am extremely enthusiastic about this book. I think it will quickly become a classic. Like Sargent's and Varian's texts, it will be a centerpiece of the core cirriculum for graduate students."--John H. Cochrane, University of Chicago
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Top Customer Reviews
Chapter 1 introduces both first order and pth order difference equations and outlines some methods of solution, such as recursive substitution. Dynamic multipliers are discussed, along with long-run and present-value calculations. Readers familiar with linear ordinary differential equations will see the similarity in solution techniques.
The next chapter introduces time series for the first time, and gives examples, both deterministic and probabilistic. Time series operators are discussed, with specific emphasis on the lag operator. The role of initial conditions for solving difference equations is outlined in detail.
After discussing the concepts of stochastic processes, stationarity, ergodicity, and white noise, in Chapter 3 the author discusses moving average processes and autoregressive processes, along with the invertibility of these processes. A few realizations of AR(1) processes are plotted explicitly.
The forecasting of time series is the topic of Chapter 4, with techniques based on conditional expectation, triangular and Cholesky factorization, and the Box and Jenkins method. An elementary example of sample and sample partial autocorrelations for US quarterly GNP growth is plotted.
The technique of maximum likelihood estimation is discussed in the next chapter, wherein the author shows how to calculate the likelihood function for various Gaussian ARMAs, along with optimization techniques. The discussion on grid searching is one of the best I have seen in the literature.
The all-important spectral analysis techniques are covered in Chapter 6 and the author does an excellent job of explaining how taking the spectrum will illustrate the contributions of periodic cycles to the variance of the data. An example of spectral analysis dealing with manufacturing data is given.
The next chapter on asymptotic distribution theory is a little bit more demanding mathematically, but the author does manage to explain the details of this theory very well. The reader can see explicitly how the central limit theorem comes into play in time series analysis.
After a review of ordinary least squares, the author gives a very rigorous discussion of linear regression models in Chapter 8. The author shows the role that heteroskedasticity plays in these techniques.
Departures from the ideal regression model are discussed further in Chapter 9, wherein the author illustrates the impact of simultaneous equations bias in contributing to the correlation of the error term with the explanatory variables. A supply and demand model from econometrics is used effectively to illustrate this contribution.
Chapters 10 and 11 discuss vector time series, with multivariate dynamical systems and vector autoregressions both treated in detail. The population coherence between two vector processes is given, along with the Newey-West, the Granger-Causality tests, and spectral-based estimators. "Green's function" techniques, via the impulse-response function , are also discussed.
Bayesian techniques, which take advantage of prior information on the sample, are discussed in Chapter 12 from both an analytical and numerical point of view. The role of Monte Carlo techniques in estimating posterior moments is unfortunately only discussed briefly.
The representation of a dynamical system in terms of state-space via the Kalman filter is treated in the next chapter. The author discusses the use of the Kalman filter in forecasting , maximum likelihood estimation, smoothing, and statistical inference. All of these tools are important in applications, and the author does a fine job of explaining them in this chapter.
The Hansen technique of generalized moments is considered in Chapter 14, with the most interesting discussion being the one on the estimation of rational expectation models. The author also shows how to use the method when nonstationary data is present.
Chapter 15 begins the study of nonstationary time series, with trend-stationary and unit root processes compared and analyzed throughout the chapter in terms of their forecast errors and their dynamic multipliers. Two other approaches to the study of nonstationary time series are also discussed in the chapter, namely, the fractionally integrated process and processes with discrete shifts in the time trend.
Processes with deterministic time trends are the subject of Chapter 16, wherein the author outlines the methods for calculating the asymptotic distributions of the coefficient estimates.
The most interesting discussion in the next chapter on univariate processes is on the Brownian walk, for it permits a more general formulation of the central limit theorem. A very detailed discussion of the Dickey-Fuller tests is given with an example of quarterly real US GNP. The Dickey-Fuller test has been widely accepted as a standard test for nonstationarity in time series. Other approaches to finding the unit roots, such as the Phillips-Perron tests are also given. The results here are generalized to the multivariate case in the next chapter.
Vector unit root processes called cointegrated processes are the subject of Chapters 19 and 20. These special time series, with each component series being I(1), are treated with respect to the implications they have on moving average, Philips triangular, common trends, and error-correction representations. An interesting application is given to exchange rate data.
Time series with variances that change over time, or heteroskedastic processes, are discussed in Chapter 21. The infamous ARCH models are fully detailed, along with their generalizations, the GARCH models.
Drastic changes in the behavior of time series is the subject of the last chapter of the book, wherein Markov chains are employed to model these kinds of time series. An application of the these models to U.S real GNP is given.
Some omissions in the book include approaches for testing covariance stationarity, such as the postsample prediction test, the CUSUM test, and the modified scaled range test.
This is a great book. Given that it has 799 pages, you must expect a lot of detail, and none of it is fluff. Not only are the procedures for constructing every kind of time series spelled out completely, but several times the author points out potential pitfalls and gives tips and tricks for circumventing them. One of them worked for me in another context and meant the difference success and failure in that project. Another benefit of the abundant detail is that, while there are recipes for each time series type, they are not written as a series of steps, but in paragraphs of detailed text. The result is you tend to understand the material, rather than just mindlessly carrying out a series of instructions. People have performed near miracles with maximum likelihood estimators, and this book tells you how it is done.
Obviously, the book is long, but another Amazon reviewer wrote that he knew exactly what kind of time series he needed, found the instructions to build it in the text, and was done in a day. Because the book has been carefully divided into chapters, sections, and sub-sections, all with clear titles and sub-titles, it is relatively quick and easy to find something, if you know what you need.
There are more recent books for sale at Amazon that claim to contain the results of the latest research on multivariate time series. While this book contains material on multivariate problems, it is presented only as an extension of single-variable situations (in what I have read; I have not finished the book). Since it is hard to avoid having several variables in a complex time series, you may want to consider the newer material.