Assignment Time Series Analysis Hamilton

Course Description

Spring 2006

Office Hours: MW 2:30 - 3:30

Eric Zivot
M228 Savery Hall

his is survey course in time series econometrics with focus on applications in macroeconomics, international finance, and finance. We will cover univariate and multivariate models of stationary and nonstationary time series in the time domain. The goals of the course are threefold: (1) develop a comprehensive set of tools and techniques for analyzing various forms of univariate and multivariate time series, and for understanding the current literature in applied time series econometrics; (2) survey some of the current research topics in time series econometrics; (3) show how to use  EVIEWS, GAUSS, MATLAB,  S-PLUS and R to estimate time series models.

The field of time series econometrics has exploded in the last decade and there is not enough time in a quarter course to comprehensively cover all of the important contributions. Consequently, we will often discuss and present results without formal proofs. Most of the gory details, however, are supplied in the textbook by Hamilton, and in the references on the reading list.

The topics we will cover this quarter include:

  • STATIONARY UNIVARIATE MODELS. Wold decomposition theorem, Difference equations, ARMA models and Box-Jenkins methodology, Model Selection, Forecasting methodology.
  • NONSTATIONARY UNIVARIATE MODELS. Trend/Cycle decomposition, Beveridge-Nelson decomposition, Deterministic and stochastic trend models, Unit root tests, Stationarity tests
  • STRUCTURAL CHANGE AND NONLINEAR MODELS.  Tests for structural change with unknown change point. Estimation of linear models with structural change. Regime switching models.
  • STATIONARY MULTIVARIATE MODELS. Dynamic simultaneous equations models, Vector autoregression (VAR) models, Granger causality, Impulse response functions, Variance decompositions, Structural VAR models.
  • NONSTATIONARY MULTIVARIATE MODELS. Spurious regression, Cointegration, Granger representation theorem, Vector error correction models (VECMs), Structural VAR models with cointegration, Testing for cointegration, Estimating the cointegrating rank, Estimating cointegrating vectors. 

Note: Those interested in more rigorous material on time series econometrics should check out Peter C.B. Phillips' homepage and the syllabi for his time series courses at Yale University.

Course Prerequisites

A good grasp of basic mathematical statistics and linear algebra is necessary for surviving the course. Some familiarity with real analysis and stochastic processes would make life easier for understanding the technical details but is not required. The mathematical appendix in Hamilton gives a very good summary of useful mathematical and statistical tools. For those with a strong interest in time series, I recommend studying graduate level probability (measure theoretic), statistics and stochastic processes in the statistics department.

A previous course in time series is not required or assumed. However, a basic knowledge of ARMA models and Box-Jenkins' methods will be helpful. I will assume that everyone remembers the time series topics covered in Econ 581 and Econ 582.

Course Requirements

Credit for this course is obtained by successfully completing

  1. All of the homework assignments (approximately 5 assignments)
  2. A medium length "replication paper", approved by me. In this paper you will attempt to replicate the results of a published or working paper
  3. Take home final exam. 


Homework problems will be posted to the web page and will be a combination of computer labs using EVIEWS and/or some matrix programming language (MATLAB, GAUSS, S-PLUS, R), and analytical problems. Detailed instructions for using EVIEWS will be provided.

For those interested in theory, I highly recommend that you do the homework problems at the end of each chapter in Hamilton (the answers are provided in the text). These problems will give you practice using the tools and techniques of time series econometrics. In addition, I encourage you to try the problems in the Problems and Solutions section of Peter Phillips' econometrics journal Econometric Theory.

Computer Lab

In this practical lab session, I will discuss the homework and computational issues. The lab will meet on Fridays between12:30 and 1:50 in SAV 211. 


Textbooks and Other Background Material

The required materials are:

  1. Time Series Analysis, by James D. Hamilton, Princeton University Press, 1994.
  2. Time Series for Macroeconomics and Finance, by John Cochrane, unpublished lecture notes, updated 2005. Available from Cochrane's web site in Adobe Acrobat
  3. Modeling Financial Time Series with S-PLUS, by Eric Zivot and Jiahui (Jeffery) Wang, Springer-Verlag, 2002.
  4. Class Readings - see syllabus page.

Some useful background material is also available in Hayashi's textbook Econometrics, which was the textbook used in Econ 583.

In addition, I will post some additional lecture material on the class web page (mostly my handwritten and typed notes).

The book by Hamilton will be our main reference source. It is a rigorous, comprehensive yet very readable treatment of topics in time series econometrics. I will often refer to Hamilton for the technical details left out of the lecture material. The notes by Cochrane provide a nice summary of time series models with applications in macroeconomics finance and is a good background source for those with little background in time series analysis. However, the notes by Cochrane do not contain much econometrics. I will fill in the gaps in lecture. Many of the chapters in Modeling Financial Time Series with S-PLUS are based on my lecture notes for this course. 

Econometrics Journals

There are many journals that carry theoretical and empirical papers using time series econometrics. Below is a selective summary. 

Theory Journals

  • Econometrica
  • Journal of Econometrics
  • Econometric Theory
  • Journal of Time Series Analysis
  • Review of Economic Studies
  • Econometric Reviews
  • Journal of the American Statistical Association
  • Biometrika
  • Applied Statistics
  • Journal of Statistical Inference and Planning
  • Econometrics Journal (electronic)

Applied Econometrics Journals

  • Journal of Business and Economic Statistics
  • Review of Economics and Statistics
  • Journal of Applied Econometrics
  • Journal of Forecasting
  • Oxford Bulletin of Economics and Statistics
  • Econometrics Journal (electronic)
  • Studies in Nonlinear Dynamics and Econometrics (electronic)
  • International Journal of Forecasting
  • Journal of Empirical Finance
  • Econometrics Letters

Field Journals with Time Series Applications

  • Journal of Monetary Economics
  • Journal of International Economics
  • Journal of International Money and Finance
  • Journal of Money, Credit and Banking
  • Applied Economics
  • Journal of Finance
  • Review of Financial Studies

*Stock, J. H., and M. W. Watson. "Implications of Dynamic Factor Models for VAR Analysis." NBER Working Paper no. 11467, 2005.

Bernanke, B. S., and J. Boivin. "Monetary Policy in a Data-rich Environment." Journal of Monetary Economics 50, no. 3 (2003): 525–46.

*Bernanke, B. S., J. Bovian, et al. "Measuring the Effects of Monetary Policy: A Factoraugmented Vector Autoregressive (FAVAR) Approach." Quarterly Journal of Economics 120 (2005): 387–422.

*Forni, M., D. Giannoni, et al. "Opening the Black Box: Structural Factor Models with Large Cross-Sections." European Central Bank, working paper 712.

Chamberlain, G., and M. Rothschild. "Arbitrage, Factor Structure and Mean-Variance Analysis of Large Asset Markets." Econometrica 51, no. 5 (1983): 1281–304.

Favero, C. A., M. Marcellino, et al. "Principal Components at Work: The Empirical Analysis of Monetary Policy with Large Datasets." Journal of Applied Econometrics 20, no. 5 (2005): 603–20.

Forni, M., M. Hallin, et al. "The Generalized Dynamic Factor Model: Identification and Estimation." Review of Economics and Statistics 82, no. 4 (2000): 540–54.

Bai, J., and S. Ng. "Determining the Number of Factors in Approximate Factor Models." Econometrica 70, no. 1 (2002): 191–221.

———. "Determining the Number of Primitive Shocks in Factor Models." Journal of Business Economics and Statistics 25 (2007): 52–60.

*———. "Instrumental Variable Estimation in a Data Rich Environment." Econometric Theory 26, no. 6 (2010): 1577–606.

Forni, M., M. Hallin, et al. "One-Sided Representations of Generalized Dynamic Factor Models." Manuscript (2011).

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