As I have moved into research, I have heard a lot of book recommendations. For now, I will collect them here. I'll add my reviews on as I read them.

- Books about Time Series
- Brockwell and Davis's Time Series: Theory and Methods: This book is my favorite book on time series. It discusses both the frequency domain and the time domain, it has a chapter on multivariate time series, and it has a few sections at the end on long memory. I have spent a long time with this book (especially the two aforementioned chapters.)
- Priestley's Spectral Analysis and Time Series. Volumes I and II in 1 book. (Probability and Mathematical Statistics): This book covers both univariate time series (Volume 1) and multivariate time series (Volume 2). I believe it provides the best coverage of cross-spectral densities and other multivariate frequency domain concepts. (It does not cover long memory time series, probably because the book predates them.) Sadly, the book is out of print.
- Bloomfield's Fourier Analysis of Time Series: An Introduction (Wiley Series in Probability and Statistics): This book is one of the classics of time series analysis. It is not as thorough as Priestley's book (above), but it does mention the analysis of multiple time series.
- Koopmans's The Spectral Analysis of Time Series (Probability and Mathematical Statistics): Yet another classic book about time series in the frequency domain.
- Hamilton's Time Series Analysis: This was the first graduate-level econometrics book I encountered. It covers a large number of topics thoroughly, though it does ignore the frequency domain entirely.
- Time Series With Long Memory (Advanced Texts in Econometrics): This book, by Peter Robsinon (one of the big names in long memory time series research), provides a good review of long memory time series and then reproduces a number of the "classic" papers in long memory time sereis (by Robinson himself and by others).
- Multiple Time Series (Wiley Series in Probability and Mathematical Statistics): This book is by E. J. Hannan, the author of many time series papers in the 1970's.
- Handbook of Time Series Analysis: Recent Theoretical Developments and Applications: This book is a compilation of articles about time series. It first caught my interest because it included a recent article by Manfred Deistler about signal extraction and factor analysis. I really like the idea of handbooks that summarize the latest knowledge in specialized fields, and there are many of them out there.
- Essays in Econometrics: Collected Papers of Clive W. J. Granger (Econometric Society Monographs) (Volume 2): Clive Granger thought about many interesting time series topics, including cointegration. This book includes a lot of his thoughts.
- Spectral Analysis of Economic Time Series (Princeton Studies in Mathematical Economics): Another more general book on time series by Clive Granger. (It is also out of print.)

- Books about longitudinal/panel data
- Econometric Analysis of Cross Section and Panel Data: This is the book I used in a course on Panel Data Econometrics. It is a bit intimidating at first, but it is thorough. This book is definitely written from the econometrics (as opposed to statistics) perspective.
- Linear Mixed Models for Longitudinal Data (Springer Series in Statistics): This book is about longitudinal data from the statistics side. This book focuses on linear models (you will need other books, such as Models for Discrete Longitudinal Data, for other models), but has some nice examples. While Wooldridge (like many economists) focuses more on fixed effects models, this book focuses more on ranodm effects models.
- Mixed Effects Models in S and S-Plus: This book is more specific to R (or S, S-Plus). I used a chapter to figure out the many diagnostic plots that you should use after fitting a linear mixed effects model.

- Books about data mining
- The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer Series in Statistics): Professor Simonoff recommends this book as an overview of data mining.

- Books about general statistics and econometrics
- Econometric Analysis: I have read only excerpts of this book, but they were well-written. Since I had the author as a professor, I can vouch for the book.
- Approximation Theorems of Mathematical Statistics: Another recommendation from Professor Hurvich. This book is a "classic" about proving asymptotic theorems.
- Mostly Harmless Econometrics: An Empiricist's Companion: This is a short book abount econometrics, and it is recommended by Andrew Gelman (a statistician at Columbia).

- Math books (that can be helpful for statistics and econometrics proofs)
- Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd Edition: Professor Hurvich recommended this book when I realized that I would have to compute standard errors based on the Hessian from maximum likelihood optimization, based on a reparameterization.
- Matrix Analysis and Topics in Matrix Analysis (both by Horn and Johnson): I came across these books on a quest for more information about the eigenvalues of Hadamard products of matrices. These books thoroughly cover advanced linear algebra - the theorems that are well-known to people in the field and that would be helpful for people using linear algebra to prove theorems, but that are not generally taught in introductory linear algebra classes. They are very handy to have around.
- Regular Variation (Encyclopedia of Mathematics and its Applications): This is a classic book on regularly varying functions. These functions (particularly slowly varying functions) are very handy for semiparametric descriptions of long memory time series (since the "short memory" part can be described by a slowly varying function instead of parametrically).

- Computer science books
- An Introduction to Iterative Toeplitz Solvers (Fundamentals of Algorithms): Raymond Chan, one of the authors of this book, has written numerous papers on the preconditioned conjugate gradient algorithm (which is the most famous iterative Toeplitz solver). This book compiles the results of research into a more convenient format.

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