Economics 240C

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TIME SERIES ANALYSIS

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Winter 2001

Instructor: / Professor Oscar Jorda
1150 Social Sciences and Humanities Bldg.
Phone: 752 7021
e-mail:
CLASS URL:
Class Meets: / M-W, 12:10-2:00 p.m. Room: WICKSON 1038
Office Hours: / Fridays 1-3, or by appointment

Course Goals: The course is intended to fulfill two needs: (1) to provide students with applied interests with the most sophisticated and up to date techniques used in empirical time series analysis, and (2) to introduce students with more theoretical inclinations to the tools that are used to derive some of the more interesting results.

Textbook: Hamilton, J. D. (1994) Time Series Analysis, Princeton University Press, New Jersey. I will follow Hamilton's book rather closely. Regardless, this is a great book, worth having in your library.

Computer Assignments: I am hoping to have 5 computer assignments that will involve the packages EViews and GAUSS. The home page for the course has a number of links to brief introductions to these programs.

Resources: Mostly, you should check the home page for the course. Additional readings for each topic can be found at the end of this document.

Grading: There will be three components to your grade, namely, assignments (30%), midterm (30%) and final (40%).

Course Outline:

  1. Introduction to Univariate, Stationary, Time Series Analysis

1.1.Introduction

1.1.1.Dynamic Multipliers, Impulse Response Functions, and Long-Run Propensity

1.1.2.Lag Operators

1.1.3.Difference Equations and Stability

1.2.Stationary ARMA Processes

1.2.1.Preliminary Concepts: Gaussian white noise, martingale difference sequences, autocovariances and autocorrelations, stationarity, ergodicity

1.2.2.Basic ARMA Models: MA models, AR models, ARMA(p,q) models, invertibility

1.3.Identification of ARMA Models

1.3.1.Common Transformations

1.3.2.Sample ACF and PACF

1.3.3.State-Space Representation of ARMA Models

1.3.4.Wold Representation Theorem

  1. Estimation and Testing

2.1.Maximum Likelihood Estimation

2.1.1.Quasi MLE: Fundamental Theorems

2.1.2.The MLE of an AR(1)

2.1.3.The MLE of a MA(1)

2.1.4.The MLE of an ARMA(p,q)

2.2.Review of Numerical Optimization

2.2.1.General Concepts

2.2.2.Review of Algorithms: Newton-Raphson, Quadratic-Hill, Gauss-Newton/BHHH, Marquardt, Davidon-Fletcher-Powell

2.3.Statistical Inference with MLE

2.3.1.Asymptotic Standard Errors

2.3.2.QMLE Standard Errors

2.3.3.Hypothesis Testing: Wald, Likelihood Ratio and LM tests; Ljung-Box/Q-Statistics

  1. Forecasting

3.1.Cost Functions

3.2.Forecasting with ARMA Models: State-Space representation

3.3.Forecasting with Non-Linear Models: Naïve, Exact, Monte-Carlo and Bootstrap forecasts

  1. Asymptotic Distribution Theory

4.1.Preliminaries: Autocovariance generating function, laws of large numbers, and the ergodic theorem

4.2.Central Limit Theorem: CLT for martingale difference sequences, and CLT for dependent processes. The Beveridge-Nelson decomposition

  1. Non-Stationary Univariate Time Series Models

5.1.Introduction: Stochastic vs. deterministic trends

5.2.Asymptotic Distribution Theory of the Non-Stochastic Trend Model

5.3.Unit Roots

5.3.1.Review: Little o, Big O, and motivation

5.3.2.Brownian Motion

5.3.3.Functional Central Limit Theorem

5.3.4.Convergence in Law for Random Functions

5.3.5.Convergence in Probability for Random Functions

5.3.6.Continuous Mapping Theorem

5.3.7.Phillips-Perron Test

5.3.8.Augmented Dickey-Fuller Test

  1. Covariance Stationary Vector Time-Series

6.1.The VAR(p) Model

6.1.1.Rewriting a VAR(p) as a VAR(1)

6.1.2.Stationarity

6.1.3.Multivariate Wold Theorem

6.1.4.VMA() Representation of a VAR(p)

6.2.Autocovariances of Vector Processes

6.3.Heteroskedasticity, Autocorrelation, Consistent, Covariance Matrix Estimation

6.3.1.The Newey-West Estimator

6.3.2.Other Estimators

  1. Causality, Feedback and Exogeneity

7.1.Granger Causality

7.1.1.Definitions and Concepts

7.1.2.Testing

7.1.3.Interpretation

7.2.Exogeneity

7.2.1.Definition and Concepts

7.2.2.Weak Exogeneity, Strict Exogeneity, and Super Exogeneity

  1. Maximum Likelihood Estimation of Vector Processes

8.1.MLE of Unrestricted VARs

8.2.Structural Models

8.3.Impulse Response Function Analysis

8.3.1.Calculating the IRF: Methods

8.3.2.Wold Causal Orderings

8.3.3.Variance Decomposition

8.3.4.Interpretation of IRFs and VDs

  1. Cointegration

9.1.Spurious Regressions

9.2.Cointegration

9.2.1.Definition and Concepts

9.2.2.Error Correction Representation

9.2.3.Granger Representation Theorem

9.2.4.Phillips Triangular Representation

9.2.5.Stock and Watson Common Trends Representation

9.3.Testing

9.3.1.Bivariate Analysis

9.3.2.Engle-Granger Test: Properties

9.3.3.Correcting Cointegration Tests for Serial Correlation

9.4.FIML Analysis of Cointegrated Systems

9.4.1.Review of Canonical Correlation Analysis

9.4.2.Johansen's Test

9.4.3.Hypothesis Testing and Estimation

  1. State-Space Models

10.1.State Space Representation of a Linear Dynamic System

10.2.Overview of the Kalman Filter

10.3.ML Estimation

10.4.Asymptotic Properties of MLE and QMLE

Additional Reading

Almost all the material for the class comes from Hamilton's book so you need not worry about the reading list except when indicated in class. The references contained in Hamilton's book are quite comprehensive if you ever need to go deeper into a topic. The references below might be helpful if you have difficulty understanding the material. An asterisk indicates references that I find particularly useful.

  1. Introduction to Univariate, Stationary, Time Series Analysis
  • Box, G.E.P. and G.M. Jenkins (1976), Time Series Analysis: Forecasting and Control, 2nd ed. San Francisco: Holden Day.
  • Gourieroux C. and A. Monfort (1997), Time Series and Dynamic Models. Cambridge: Cambridge University Press.
  • *Sargent, T. J. (1987), Macroeconomic Theory. Boston: Academic Press. (Chapters 9, 10, and 11).
  1. Estimation and Testing
  • *Amemiya, T. (1985), Advanced Econometrics. Cambridge: Harvard University Press. (Chapter 4).
  • *Davidson, R. and J. G. MacKinnon (1993) Estimation and Inference in Econometrics. Oxford: Oxford University Press. (Chapter 8).
  • *Engle, R. F. (1984), "Wald, Likelihood Ratio, and Lagrange Multiplier Tests in Econometrics," Ch. 13 in Handbook of Econometrics, Vol. II, eds. Z. Griliches and M.D. Intrilligator, Amsterdam: North-Holland.
  • *Greene, W. H. (1997) Econometric Analysis, 4th Edition. New Jersey: Prentice Hall. (Chapter 5).
  1. Forecasting
  • *Granger, C. W. J. and P. Newbold, (1986) Forecasting Economic Time Series. Academic Press.
  1. Asymptotic Distribution Theory
  • Davidson, J. (1994) Stochastic Limit Theory. Oxford; Oxford University Press.
  • *White, H. (1999) Asymptotic Theory for Econometricians. Revised Edition. San Diego: Academic Press
  • van der Vaart, A. W. (1998) Asymptotic Statistics. Cambridge: Cambridge University Press.
  1. Non-Stationary Univariate Time Series Models
  • * Davidson, J. (1994) Stochastic Limit Theory. Oxford; Oxford University Press.
  • Dickey, D. A. and W. A. Fuller (1979), " Distribution Estimators for Autoregressive Time Series with a Unit Root," Journal of the American Statistical Association, 74, 437-431.
  • Phillips, P.C.B. (1986), "Time Series Regression with Unit Roots," Econometrica, 55, 227-302.
  • Phillips, P.C.B. (1998), "New Tools for Understanding Spurious Regressions," Econometrica, 66, 1299-1236.
  • *Stock, J. H. (1994), "Unit Roots, Structural Breaks, and Trends," in Handbook of Econometrics, Vol. IV, eds. D. McFadden and R. F. Engle. Amsterdam: North-Holland.
  • * Tanaka, Katsuto, (1996) Time Series Analysis. New York: John Wiley (Chapter 3 and Chapter 9).
  1. Covariance Stationary Vector Time-Series
  • Den Haan, W. J. and A. Levin, (1997), " A Practioner's Guide to Robust Covariance Matrix Estimation," Handbook of Statistics 15 (Chapter 12, 291-341)
  • *Den Haan, W. J. and A. Levin, (1996), " Inferences from Parametric and Non-Parametric Covariance Matrix Estimation Procedures," NBER Technical Working Paper 195.

Both papers can be downloaded from:

  • Newey W. N. and K. D. West (1987), "A Simple Positive Semi-Definite Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, 55, 703-708.
  1. Causality, Feedback and Exogeneity
  • *Engle, R. F., D. F. Hendry, and J.-F. Richard, (1983), "Exogeneity," Econometrica, 51, 277-305.
  • *Granger, C. W. J. (1980), "Testing for Causality: A Personal Viewpoint," Journal of Economic Dynamics and Control, 2, 329-352
  • Granger, C. W. J. (1989), Modelling Economic Series, Oxford: Oxford University Press.
  • *Hendry, D. F. (1995), Dynamic Econometrics, Oxford: Oxford University Press.
  • Hoover, K. D. and S. M. Sheffrin, (1992), " Causation, Spending, and Taxes: Sand in the Sandbox or Tax Collector for the Welfare State?" American Economic-Review; 82(1), 225-48.
  • Swanson, N. R. and C. W. J. Granger, (1997), "Impulse Response Functions Based on a Causal Approach to Residual Orthogonalization in Vector Autoregressions," Journal of the American Statistical Association, 92(437), 357-367.
  • Demiralp S. and K. D. Hoover, (2000), “Structural VARs,” U.C. Davis, manuscript.
  1. Maximum Likelihood Estimation of Vector Processes
  • *Reinsel, G. C. (1993), Elements of Multivariate Time Series Analysis, New York: Springer-Verlag.
  1. Cointegration
  • *Engle, R. F. and C. W. J. Granger, (1991), Long-Run Economic Relationships, Oxford: Oxford University Press.
  • *Johansen, S. (1995), Likelihood-Based Inference in Cointegrated Vector-Autoregressive Models, Oxford: Oxford University Press.
  • *Sims, C. A., J. H. Stock and M. W. Watson, (1990), "Inference in Time Series Models with some Unit Roots," Econometrica, 58, 113-44.
  • Watson, M. W. (1994), "Vector Autoregressions and Cointegration," in Handboof of Econometrics, Vol. IV, eds. D. McFadden and R. F. Engle. Amsterdam: North-Holland.
  1. State-Space Models
  • *Hamilton, J. D. (1994), "State-Space Models," in Handbook of Econometrics, Vol. IV, R. F. Engle and D. L. McFadden, eds. Amsterdam: North-Holland.
  • Harvey, Andrew C. (1989), Forecasting Structural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press.

Time Series Econometricians in Davis

  • Arthur M. Havenner, Professor, Department of Agricultural and Resource Economics.
  • Web-site:
  • Research Interests: Econometrics, both classical and time series analysis, involving any aspects of hypothesis testing, policy simulation / optimal control, and forecasting. If you have any questions about State Space modeling and the Kalman filter, he is your man.
  • Books:Applications of Computer Aided Time Series Modeling, M. Aoki and A. Havenner, (eds.). Berlin: Springer-Verlag, 1997.
  • Prasad Naik, Assistant Professor, Graduate School of Management. Although professor Naik is formally professor in Marketing, he has a lot of experience in time series modeling, forecasting and control.
  • Web-site:
  • Research Interests: advertising strategy, consumer choice behavior, sales forecasting, dynamic market response models.
  • Robert Shumway, Professor, Department of Statistics.
  • Web-site:
  • Research Interests: applications of multivariate spectral analysis to high dimensional problems in discrimination and clustering for multivariate time series and to linear filter contrasts arising in a multivariate analysis of variance. Analysis of incomplete data that can be modeled in terms of linear and nonlinear state-space models.
  • Books: Shumway, R.H. (1988). Applied Statistical Time Series Analysis. Englewood Cliffs, New Jersey: Prentice Hall.

Shumway, R.H. & Stoffer, D. S. (2000). Time Series Analysis and Its Applications. New York: Springer.

  • Chih-Ling Tsay, Professor, Graduate School of Business.
  • Web-site:
  • Research Interests: application of statistics in business, regression diagnostics, model selection, optimal design.
  • Books:Regression and Time Series Model Selection, with Allan McQuarrie, World Scientific, 1998.

Time Series Topics

Here is a potpourri of other topics that we will not discuss in class. There is no particular order and were possible, I enclose relevant references.

  1. Time Series Topics in Finance
  • Campbell, John Y., A. W. Lo, and A. C. MacKinlay, (1997), The Econometrics of Financial Markets. Princeton University Press.
  • Mills, T. C. (1993), The Econometric Modelling of Financial Time Series. Cambridge University Press.
  1. ARCH Models and Stochastic Volatility Models
  • Engle, R. F. (1995), ARCH Selected Readings, Oxford University Press
  • Shepard, N., S. Kim., and S. Chib (1998), “Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models,” Review of Economic Studies, 65, 361-393.
  • Continuous Time Models
  • Bergstrom, A. R. (1990), Continuous Time Econometric Modelling, Oxford University Press.
  • Neural Networks
  • White, H. (1992), Artificial Neural Networks: Approximation and Learning Theory. Blackwell Publishers.
  • Time Series Duration Models
  • Engle, R. F. and J. R. Russell, (1998), “Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data,” Econometrica, V. 66, N. 5, 1127-1162.
  • Jorda, O. and M. Marcellino, (2000), “Stochastic Processes subject to Time Scale Transformation: An Application to High Frequency FX Data,” UC Davis working paper 00-02.
  1. Time Series Topics in Macroeconomics
  2. Nonlinear Time Series Models
  • Granger, C. W. J. and T. Terasvirta (1993), Modelling Nonlinear Economic Relationships, Oxford University Press.
  • Markov Switching Regimes Models
  • Hamilton, J. D. (1989), “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle,” Econometrica, 57(2), 357-384
  • Kim, C. J. and C. R. Nelson, (1999), State Space Models with Regime Switching, MIT Press.
  • Threshold Autoregressive and Smooth Transition Models
  • Tong, H. (1983), Threshold Models in Non-Linear Time Series Analysis, Springer-Verlag
  • Terasvirta, T. (1994), “Specification, Estimation and Evaluation of Smooth Transition Autoregressive Models,” Journal of the American Statistical Association.
  • Discrete-Time, Time Series Duration Models: The ACH Model
  • Hamilton, J. D. and O. Jorda, (2000), “A Model for the Federal Funds Rate Target.” NBER working paper 7847.
  • Demiralp, S. and O. Jorda, (2000), “The Pavlovian Response of Term Rates to Fed Announcements,” UC Davis, working paper 99-06R.
  • Structural Break Testing
  • Bai, J. and P. Perron, (1998), “ Estimating and Testing Linear Models with Multiple Structural Changes,” Econometrica, 66(6), 47-78.
  • Causality in Macroeconomics
  • Demiralp, S. (2000), The Structure of Monetary Policy and Transmission Mechanism, UC Davis Thesis.
  • Hoover, K. D. (2001), Causality in Macroeconomics, Cambridge University Press.

  1. Other Topics
  2. Time Aggregation
  • Jorda, O. and M. Marcellino, (2000), “Stochastic Processes subject to Time Scale Transformations: An Application to High-Frequency FX Data,” UC Davis, working paper 00-02.
  1. Simulation Methods for Time Series Models
  2. Kim, C. J. and C. R. Nelson, (1999), State Space Models with Regime Switching, MIT Press.
  3. Gourieroux, C. and A. Monfort, (1996), Simulation Based Econometric Methods, Cambridge University Press.
  4. Bootstrap in Time Series
  • Berkowitz, J. and L. Kilian (2000), “Recent Developments in Bootstrapping Time Series,” Econometric Reviews, 19(1), 1-48.
  1. Spectral Analysis and Wavelets
  • Percival, D. B. and A. T. Walden, (2000), Wavelet Methods for Time Series Analysis, Cambridge University Press
  1. Dynamic Panel Data Models
  2. Arellano, M. and B. Honore, (1999), “Panel Data Models: Some Recent Developments,” prepared for the Handbook of Econometrics, Vol. 5.

Additional Resources

I recommend that you visit Eric Zivot’s home page. He has collected numerous interesting links if you are interested in time series. This is his web-site:

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