Course Description

This course introduces students to the time series methods and practices which are most relevant to the analysis of economic and financial time series 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 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 time series tools in applications using the software such as EViews, Ox, PcGive, and JMulti.

Given the time limitations of a one semester course the topics that we will cover will necessarily be selective. Econometric time series literature is vast and continuously growing with new developments. The topics that will be covered are most relevant for applied research and are long standard tools of time series econometrics.

It is my belief that the best way to learn the techniques needed for research in applied macroeconomics is by doing. The practical component of this course will include data collection and using computer programs. You will be given several assignments that can be completed using one of the software packages you are familiar with. It is very rare for modern econometric packages to have commands to do all the things you would want to do in this course. Therefore, it may be necessary to write your own computer code to complete assignments that are given. I do not require students to use any one computer language of package but I do require students to give me properly documented programs or outputs as part of an answer to any assignment given in this class.

The field of time series econometrics has exploded in the last two decades and there is not enough time in a one semester 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. Students who are seeking rigorous treatment of the some topics should refer to the Hamilton’s book and the papers on the reading list.

The topics we will cover this course include:

Stationary Univariate Models. Wold decomposition theorem, Difference equations, Smoothing, Seasonal Adjustment, 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. GARCH Models, 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.

Course Attitude

More than other courses, this course tries to deal with the genuine subtlety of honest data analysis and the often misunderstood role that mathematical models play in our understanding of empirical data.

Students will be given fundamental grounding in the use of some widely used tools, but much of the energy of the course is focus on individual investigation of time series. Active participation in the class is very important. This class is more about the opportunity for individual and team discoveries than it is about mastering a fixed set of techniques.

Course Prerequisites

This course assumes no prior knowledge of any aspect of time series analysis. Although previous course in time series is not required or assumed, a basic knowledge of ARMA Students will need to be generally comfortable with statistical inference and with the basic regression model from the standard econometric tradition. 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 to follow our econometrics program.

Course Requirements

Credit for this course is obtained by successfully completing

1. All of the homework and lab assignments (20 percent)
2. A medium length “term paper” on a topic approved by me (20 percent)
3. A midterm exam (20 percent)
4. A final exam (40 percent)

Homework

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

Textbooks and Other Background Material

The required materials are

1. An Introduction To Applied Econometrics: A Time Series Approach, by Kerry Patterson, Palgrave, 2000. (P)
2. Applied Time series Econometrics, by Helmut Lutkepohl and Makus Kratzig, Cambridge University Press, 2004. (LK)
3. Time Series Analysis, by James D. Hamilton, Princeton University Press, 1994. (H)
4. Time Series for Macroeconomics and Finance, by John Cochrane, unpublished lecture notes, updated 2005. Available from Cochrane's web site in Adobe Acrobat. (C)
5. Class Readings - see the listing on the web page.

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

The book by Patterson, Lutkepohl and Kratzig, and Hamilton will be our main reference source. Hamilton’s book 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. The books by Patterson and, Lutkepohl and Kratzig are very readable application oriented textbooks. I will often refer to the applications in these books. JMulti is a user friendly free software accompanying Lutkepohl and Kratzig. All time series techniques covered in Lutkepohl and Kratzig are implemented in JMulti. Please refer to Chapter 8 of Lutkepohl and Kratzig for further details on JMulti.

Course Outline

Since some of the recent developments in time series are not covered in the book, I will also rely on journal articles, which are listed in the course outline below. You are only required to read the articles that I will discuss in class, which are marked by †. The remaining articles are for your reference, if you want to deepen your understanding of certain topics. The required readings are marked by *. The readings marked by ‡ are recommended.

1. Univariate Time Series

(a) Models of the conditional mean

i. Stationary time series

     • ARMA models

          ‡P, Section 3.4
         *LK, Section 2.1-2.6, 2.8-2.10
          ‡C, Chapter 3-6
          ‡H, Chapters 1-3, 5

      • Seasonal adjustment: Classical decomposition, X11/X12 seasonal filters

           *Lecture notes

ii. Non-stationary time series

     • Tests for structural breaks

Andrews, D.W.K., Ploberger, W. (1994): "Optimal Tests When a Nuisance Parameter is Present Only Under the Alternative", Econometrica, 62, 1383-1414

 Bai, J. (1997): "Estimating Multiple Breaks One at a Time", Econometric Theory,

13, 315-352

 Bai, J., Perron, P. (1998): "Estimating and Testing Linear Models with Multiple

Structural Changes", Econometrica, 66, 47-78

 *Hansen, B. (2001): "The New Econometrics of Structural Change: Dating Breaks in U.S. Labor Productivity", Journal of Economic Perspectives, 15, 117-128 

     • Random walks and unit root testing 

          *P, Chapter 6, Section 7.6-7.8‡LK, Section 2.7
          ‡C, Chapter 10
          ‡H, Chapters 15, 17

 Campbell, J. and G. Mankiw (1987), "Are Output Fluctuations Transitory?," American Economic Review.

*Campbell, J.Y. and P. Perron (1991), "Pitfalls and Opportunities: What Macroeconomists Should Know About Unit Roots," NBER Macroeconomics Annual, Cambridge, MA: MIT Press.

Clark. P.K. (1987), "The Cyclical Component of U.S. Economic Activity," Quarterly Journal of Economics. Available in JSTOR.

Cochrane, J. H. (1988). How big is the random walk in gnp?, Journal of Political Economy 96: 893–920.

Hylleberg, S., Engle, R. F., Granger, C. W. J. & Yoo, S. (1990). Seasonal integration and cointegration, Journal of Econometrics 44: 215–238.

Morley, J., C.R. Nelson and E. Zivot (2003), "Why are Beveridge Nelson and Unobserved Components Decompositions of GDP so Different?," Review of Economics and Statistics.

†Nelson, C.R. and C.I. Plosser (1982), "Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications," Journal of Monetary Economics, 10, 139-162.

Stock, J.S. and M.Watson (1988), "Variable Trends in Economic Time Series," Journal of Economic Perspectives, Vol 2, No. 3. Available in JSTOR.

Elliott, G., Rothemberg, T.J., Stock, J.H. (1996): "Efficient Tests for an Autoregressive Unit Root", Econometrica, 64, 813-836

 Stock, J.H. (1994): "Unit Roots and Trend Breaks", Handbook of Econometrics, vol. IV, Chapter 46 (downloadable from http://www.elsevier.com/hes/books/02/menu02.htm)

 Zivot, E. & Andrews, D. W. K. (1992). Further evidence on the great crash, the oil-price shock, and the unit-root hypothesis, Journal of Business & Economic Statistics 10: 251–270.

      • Trend/cycle decomposition 

* Lecture notes. 

M. Baxter and R.G. King. (1999). Measuring business cycles: Approximate bandpass filters. The Review of Economics and Statistics, 81(4):575–93.

Beveridge, S. and C.R. Nelson (1981), "A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the Business Cycle," Journal of Monetary Economics, 7, 151-74.  

L. Christiano and T.J. Fitzgerald. (2003). The bandpass filter. International Economic Review, 44(2):435–65. 

R.J. Hodrick and E.C. Prescot. (1997). Postwar US business cycles: an empirical investigation. Journal of Money, Credit, and Banking, 29(1):1–16. 

(b) Models of the conditional variance 

     • ARCH/GARCH 

          *P, Chapter 16
          ‡LK, Chapter 5
          ‡H, Chapter 21 

Bollerslev, T., Engle, R.F., Nelson, D.B. (1994): "ARCH Models", Handbook of Econometrics, vol. IV, Chapter 49 (downloadable from http://www.elsevier.com/hes/books/02/menu02.htm) 

Engle, R.F. (1982): "Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of U.K. Inflation", Econometrica, 50, 987-1008 

Bollerslev, T. (1986): "Generalized Autoregressive Conditional Heteroskedasticity", Journal of Econometrics, 31, 307-327

2. Multivariate Time Series 

(a) Stationary time series 

     • VAR, impulse-response functions, variance decomposition 

‡P, Chapter 14.2
*LK, Chapter 3
‡C, Chapter 7
‡H, Chapter 11 

Cooley, T. B. & LeRoy, S. F. (1985). A theoretical macroeconometrics: A critique, Journal of Monetary Economics 16: 283–308. 

Litterman, R. B. (1986). Forecasting with bayesian vector autoregresion: Five years of experience, Journal of Business & Economic Statistics 4: 25–38. 

Litterman, R. B. & Weiss, L. (1985). Money, real interest rates, and output: A reinterpretation of postwar U.S. data, Econometrica 53: 129–156. 

Lutkepohl, H. (1990). Asymptotic distributions of impulse response functions and forecast error variance decomposition of vector autoregressive models, Review of Economics and Statistics 72: 116–125. 

Runkle, D. (1987). Vector autoregression and reality, Journal of Business & Economic Statistics 5: 437–432. 

Sims, C. A. (1980). Macroeconomics and reality, Econometrica 48: 1-48. 

     • Granger causality 

*LK, Chapter 3.7
‡C, Chapter 7.5
‡H, Chapter 11.2 

Granger, C.W.J. (1969): "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods", Econometrica, 37, 424-438. 

(b) Non-stationary time series 

     • Spurious regressions 

*P, Chapter 8.2
‡H, Chapters 18.3 

Durlauf, S. N. & Phillips, P. C. B. (1988). Trends versus random walks in time series analysis, Econometrica 56: 1333–1354. 

Granger, C.W.J., Newbold, P. (1974): "Spurious Regressions in Econometrics", Journal of Econometrics, 2, 111-120. 

Phillips, P. C. B. (1986). Understanding spurious regressions in economics, Journal of Econometrics 33: 311–340. 

     • Cointegration 

*P, Chapter 8,14
‡LK, Chapter 3
‡C, Chapter 11
‡H, Chapter 19 

Campbell, J. Y. & Shiller, R. J. (1987). Cointegration and tests of present value models, Journal of Political Economy 95: 1062–1088. 

†Engle, R.F., Granger, C.W.J. (1987): "Co-Integration and Error Correction: Representation, Estimation and Testing", Econometrica, 55, 251-276 

Johansen, S. (1988). Statistical analysis of cointegration vectors, Journal of Economic Dynamics and Control 12: 231–254. 

Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models, Econometrica 59: 1551–1580. 

Johansen, S. (1992a). Determination of cointegration rank in the presence of a linear trend, Oxford Bulletin of Economics and Statistics 54: 383–397. 

Johansen, S. (1992b). A representation of vector autoregressive processes integrated of order 2, Econometric Theory 8: 188–202. 

Johansen, S. (1995). Likelihood-Based Inference in Cointegrated Vector Auto-Regressive Models, Oxford University Press. 

†Johansen, S. & Juselius, K. (1990). Maximum likelihood estimation and inference on cointegration-with applications to demand for money, Oxford Bulletin of Economics and Statistics 52: 169–210. 

Johansen, S. & Juselius, K. (1992). Testing structural hypothesis in a multivariate cointegration analysis of the ppp and uip of uk, Journal of Econometrics 53: 211–244. 

Phillips, P. C. B. (1991). Optimal inference in cointegrated systems, Econometrica 59: 283–306. 

Phillips, P. C. B. (1994). Some exact distribution theory for maximum likelihood estimators of cointegration coefficients in error correction models, Econometrica 62: 73–94. 

Stock, J. H. (1987). Asymptotic properties of least squares estimators of cointegrating vectors, Econometrica 55: 1035–1056. 

†Stock, J. H. & Watson, M. W. (1988). Testing for common trends, Journal of the American Statistical Association 83: 1097–1107. 

†Watson, M.W. (1994): "Vector Autoregressions and Cointegration", Handbook of Econometrics, vol. IV, Chapter 47, sections 1 and 2 (downloadable from

http://www.elsevier.com/hes/books/02/menu02.htm) 

3. Elements of forecasting  (if time permits)  

     • Forecasting with regression models 

* Lecture notes
‡H, Chapter 4 

     • Model selection and information criteria 

*Granger, C.W.J., King, M.L., White, H. (1995): "Comments on the Testing of Economic Theories and the Use of Model Selection Criteria", Journal of Econometrics, 67, 173-187 

     • Forecast evaluation and Combination 

*Diebold, F.X., Lopez, J.A. (1996): "Forecast Evaluation and Combination", in The Handbook of Statistics, Volume 14: Statistical Methods in Finance, eds. G.S. Maddala and C.R. Rao, 241-268. Amsterdam: North-Holland. (working paper version downloadable at:

http://www.ssc.upenn.edu/~fdiebold/papers/paper9/paeva.pdf) 

Granger, C. W. J. (1999): Empirical Modeling in Economics: Specification and Evaluation, Cambridge University Press, New York 

White, H. (2000): "A Reality Check for Data Snooping", Econometrica, 68, 1097-1126 

     • Forecasting with many predictors: data-reduction methods 

Hoover, K. D., Perez, S. J. (1999): “Data Mining Reconsidered: Encompassing and the General-to-Specific Approach to Specification Search”, Econometrics Journal, 2, 167-191 

Litterman, R. B. (1986): “Forecasting with Bayesian Vector Autoregressions - Five Years ofExperience”, Journal of Business and Economic Statistics, 4, 25-38

Stock, J. H., Watson, M. W. (2002): “Macroeconomic Forecasting Using Diffusion Indexes”, Journal of Business and Economic Statistics, 20, 147-162 

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