Time Series Analysis

I’ve been reading Time Series Analysis (‘Hamilton’) for 6 months. Today I officially finished reading the book. Last year, I finished Microeconomic Theory (’MWG’, Microeconomic Theory ) and Time Series Analysis, both of which have greatly transformed my understanding regarding economic theory. This is the first time I’ve read a textbook so thoroughly and even solved every single problem after each chapter since college. I read it on numerous subway journeys to home, to school and to office, standing mostly. I read it in the beloved Old Hall of Tsinghua Library, during class breaks at Wudaokou, and at my office desk when I’ve done my work as a central banker. I read it late into the night, when my family all fell asleep, only the dim light from desk lamp as my sole companion. Hardcover Hamilton became softcover and covered by adhesive tape. A white-turned-grey Hamilton of 799 pages and a solution manual of 63 pages are the by-products. Although the manual contains many errors and some proofs are not as simple as appendix, when looking at it, as well as the book itself, it feels amazing. I’ve finally done it. Some thought as Ph.D., we should read papers instead of textbooks. It’s also ‘boring’ and sufficiently daunting to read those monographs. But as a newcomer to economic theory, considering my background of both math/physics and finance, I choose to start my career as an economist by reading classics. Every Ph.D. should be responsible for his own training. After reading several classic text book written by economics gurus, I’m so glad that I’ve made the right decision. Hamilton is not only about time series, but also major areas of econometrics. I found it much more superior than any book of econometrics I’ve read. It covers maximum likelihood estimation, asymptotic theory, general least squares, VAR, Bayesian Analysis, General Method of Moments, Cointegration, ARCH, GARCH, IGARCH and many other general topics covered in advanced econometrics courses. It’s cogent, coherent, rigorous, and most importantly, beautiful. I can’t talk the beauty of Hamilton, but I can name several important chapters. First several chapters are easy and pieces of cakes. Chapter 5 shows abundant numerical optimization techniques, which will blow up your mind for the first time. Chapter 7 is about asymptotic theory. This is the heart of advanced econometrics and repeatedly referenced to through the book. Chapter 8 instilled a whole semester of Advanced Econometrics I which we took last year into 28 pages. These two chapters are the next major blow-your-mind point. Chapter 13 (Kalman Filter) is the first major obstacle readers might encounter. Chapter 17 and 18 cover asymptotic theory for nonstationary time series. Chapter 17 and 19 are not only long, but also freaking difficult. Chapter 20 wraps up nonstationary time series. I find math proof in it truly splendid. Chapter 21 and 22 are the last chapters and written like poems, or musical notes. Yes, sipping through ARCH, GARCH, IGARCH, EGARCH is turned into poem-reading by Mr. Hamilton. I thank him very much for this. For so many years, when I heard about any-ARCH, I frowned. Now I’m more than happy to hear the ARCH family. Hamilton is hard. Reading speed diverged much during last 6 months. I could finish tens of pages per day, but most of the time, only several pages per day. When reading Chapter 19, I found it so hard that I forgot what the just turned page told. In Chinese, we call it ‘Duanpian('')’. For most of the chapters, I must read more than 3 times to gain a basic understanding. I read a little bit slowly not because Mr. Hamilton is a bad writer, but because the content itself. If you have read Greene’s Econometrics Analysis, you’ll find Hamilton more Ph.D.-friendly. Once when I was asked about what books to choose for the entrance exam of Ph.D. of PBC School of Finance in Tsinghua University, I would tell them several econometrics textbooks written in Chinese, such as CHENG Qiang’s or JIN Yunhui’s. Now I will definitely recommend Hamilton. Time Series Analysis by James D. Hamilton is simply the green card to econometrics.

Book ownership of Time Series Analysis is about an month and a half, but reading it has occurred only in the last two weeks. 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.

This book is the only self-sufficient option to study time series analysis at this level of mathematical detail. Hamilton does not need anything from advanced mathematics to understand: linear algebra (Strang) plus probability theory (non-measure theoretic) is enough. The book is ranging from challenging to very challenging, but it is related to general understanding of mathematics, not the prerequisites. However, there is NO OTHER option at this level of PROOF DETAIL and QUALITY of EXPLANATION. Whenever needed, the author introduces new pages and chapters, instead of dropping famous "proof is left to the reader" or "it is obvious". Reading might take a year or more, but at least it is quality reading, and material is really broad. Newer things are easy to catch up to after learning all the mathematical tools Hamilton presents in his book. In order to compare, I tried to read Brockwell and Davis (introduction to Time Series Analysis, not his other measure theoretic text), and was completely lost. Hamilton explains the same things using more space, but rigorously and completely, unlike Brockwell and Davis ("proof in the exercise", "here is a symbol that denotes thing X which is derived from thing Y which correlates with thing Z, Z is obvious to show", "easy to show" right in the middle of all results). The other text by Brockwell is too advanced for any person without mathematical degree. The book by Hyndman available online is too basic, and has no mathematical theory. So also not a competitor.

Ottima rilegatura, veramente un gioiello

Extremely thorough and complete book. Requires some technical proficiency but the mathematical annexes are very well done. I highly recommend This book. Very well organised with well chosen examples. An essential up to date reference book.

Delivered in excellent condition. A definitive must-read for anyone serious about time series analysis.

great book - read it from cover to cover. Believe me, despite being written in 1994 there are really few who give you the same level of comprehensible detail. must have (and read) by any decent statistician

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