Department of Economics Rustam Ibragimov

Harvard University James H. Stock

Fall 2009
ECONOMICS 2142
TIME SERIES ANALYSIS

Syllabus

This course examines the models and statistical techniques used to study time series data in
economics. The course has two specific objectives. The first is to equip students who anticipate
using time series data in their Ph.D. research with the tools they need for state-of-the-art empirical
research. The second objective is to lay out the econometric theory of time series analysis, with an
emphasis on recent developments. Problem sets will have both theoretical and empirical
components. The substantive applications in the course will draw primarily from macroeconomics
and finance.

All the topics covered in the course are relevant to empirical applications. The course is organized
so that the most important tools for applied researchers are presented first, without unnecessary
mathematical formalities. Only a few of the papers listed under a topic will be covered; one role of
this syllabus is to list additional references for those wishing to delve into specific topics in greater
detail.

There will be two problem sets containing both theoretical and computational work, plus a final
research paper. The final grade will consist solely of your grades on the problem sets and paper
(25% weight on each problem set, 50% weight on paper). You are encouraged to work together on
the problem sets, but you should write up problem set solutions on your own. The paper should
make a new contribution to the literature on a topic of your choosing related to those covered in the
course. Unless given explicit permission otherwise, the final research paper shall be sole authored.
The paper can be either theoretical or empirical, and some topics will be suggested over the course
of the semester.

Textbooks
The primary texts are Hamilton (1994) (for models and methods) and Hayashi (2000) (for GMM
and basic limit theorems). The later sections of the course contains material not covered (at least
not well) in textbooks and draws heavily on articles. In any event, the lectures will be self-
contained.

Hamilton, J.D., Time Series Analysis. Princeton: Princeton University Press, 1994. (or
latest edition)

Hayashi, Fumio, Econometrics. Princeton: Princeton University Press, 2000.

Economics 2142 Fall 2009

Supplemental Texts (more specialized)

Brillinger, D.R, Time Series Data Analysis and Theory, second edition. New York: Holt,
Rinehart and Winston, 1981. (A classic text for spectral estimation and filtering,
with an engineering/statistics orientation.)

Brockwell, P.J. and R.A. Davis, Time Series: Theory and Methods. New York: Springer-
Verlag, 1987. (An advanced survey of time series techniques from the point of view
of engineers and statisticians. Perhaps the most complete treatment of linear time
series models [univariate and vector ARMA models].)

Canova, Fabio, Methods for Applied Macroeconomic Research, Princeton University Press,
2007. (DSGEs, structural VARs, and related topics)

Davidson, J., Stochastic Limit Theory. Oxford: Oxford University Press, 1994. (A
thorough but accessible treatment of central limit theorems and convergence on
function spaces.)

DeJong, David N. and Chetan Dave (2007), Structural Macroeconometrics, Princeton

University Press. (A good treatment of DSGEs)

Hall, A.R., Generalized Method of Moments, Oxford: Oxford University Press, 2004
(Everything you every wanted to know and more about GMM under classical
asymptotics.)

Hall, P. and C.C. Heyde, Martingale Limit Theory and its Applications. New York:
Academic Press, 1980. (The classic treatment of martingales and convergence on
function spaces.)

Harvey, A.C., Time Series Models, Second Edition. Cambridge: MIT Press, 1993. (A
concise overview of time series tools, with an emphasis on modeling, numerical
implementation and the Kalman filter, and not much distribution theory.)

Hatanaka, M., Time-Series-Based Econometrics: Unit Roots and Cointegration. Oxford:

Oxford University Press, 1996. (Another perspective on the unit roots/cointegration
literature, well organized and reasonably comprehensive.)

Stock, J.H. and M.W. Watson, “What’s New in Time Series Econometrics,” NBER mini-
course, slides at http://www.nber.org/confer/2008/si2008/tseprg.html

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Economics 2142 Fall 2009

Course Outline

Primary readings are denoted by “*”.

1. Fundamentals of second order stationary time series

Brockwell and Davis, Chs. 1, 3, Sect. 5.7
*Hamilton, Chs. 1-5, 7, 13.
Harvey, Chs. 1, 2.1-2.5, and 6

2. The spectrum and linear filtering theory in the frequency domain

Brockwell and Davis, Ch.4, 6, 10
*Hamilton, Ch. 6
Harvey, Ch. 3
Brillinger, Chs. 3-5

3. Inference and model selection in linear time series models

*Berk, K.N. (1974), “Consistent Autoregressive Spectral Density Estimates,” Annals of
Statistics 2, 489-502.
*Geweke, J. and R. Meese (1981), “Estimating Regression Models of Finite but Unknown
Order,” International Economic Review 22, no. 1, 55-70.
*Hamilton, Ch. 7; Hayashi, Chapter 2

4. Asymptotics I: Empirical Processes and Functional Central Limit Theory

*Andrews, D.W.K. (1994), “Empirical Process Methods in Economics,” Handbook of
Econometrics, v. IV, 2247-2294.
Hall and Heyde, ch. 4.
*Stock, J.H. (1994), “Unit Roots and Trend Breaks,” Handbook of Econometrics, v. IV,
section 2.
5. Structural Breaks
5a. Testing
Andrews, D.W.K. and W. Ploberger (1994), “Optimal Tests When a Nuisance Parameter is
Present Only Under the Alternative,” Econometrica, 62, 1383-1414.
Elliott, G. and U.K. Müller (2006), “Efficient Tests foor General Peristent Time Variation
in Regression Coefficients,” Review of Economic Studies, 73, 907-940.
Nyblom, J. (1989), “Testing for the Constancy of Parameters Over Time,” Journal of the
American Statistical Association, 84, 223-30.
5b. Estimation
Bai, J. (1997), “Estimation of a Change Point in Multiple Regressions,” Review of
Economics and Statistics, 551-563.
Bai, J. (1997), “Estimating Multiple Breaks One at a Time,” Econometric Theory 13, 315-
352.
Bai, J. and P. Perron (1998), “Testing for and Estimation of Multiple Structural Changes,”
Econometrica, 47-78.
Bai, J., R.L. Lumsdaine, and J.H. Stock (1998), “Testing for and Dating Common Breaks in
Multivariate Time Series,” Review of Economic Studies 63, 395-432.

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Economics 2142 Fall 2009

Eo, Y. and Morley, J. (2008), “Likelihood-Based Confidence Sets for the Timing of
Structural Breaks,” manuscript, Washington University of St. Louis.
*Hansen, B. (2001), “The New Econometrics of Structural Change: Dating Breaks in U.S.
Labor Productivity,” Journal of Economic Perspectives, 15, no. 4, 117–128.

6. Heteroskedasticity and autocorrelation consistent (HAC) variance estimation

*Andrews, D.W.K. (1991), “Heteroskedasticity and Autocorrelation Consistent Covariance
Matrix Estimation,” Econometrica 59, 817-858.
Andrews, D.W.K. and J.C. Monahan (1992), “An Improved Heteroskedasticity and
Autocorrelation Consistant Covariance Matrix Estimator,” Econometrica 60, 953-
966.
*den Haan, W.J. and A. Levin (2000), “Robust Covariance Matrix Estimation with Data-
Dependent VAR Prewhitening Order,” NBER Technical Working Paper #255.
den Haan, W.J. and A. Levin (199?), “A Practitioners Guide to Robust Covariance Matrix
Estimation,” Handbook of Statistics 15, ch. 12, 291-341.
Hansen, C. (2007), “Asymptotic Properties of a Robust Variance Matrix Estimator for Panel
Data when T is Large” Journal of Econometrics, December.
Ibragimov, R. and Müller, U.K. (2007), “t-statistic based correlation and heterogeneity
robust inference,” manuscript, Harvard University
Jansson, M. (2004), “The Error in Rejection Probability of Simple Autocorrelation Robust
Tests,” Econometrica, 72, 937-946.
Kiefer, N., T.J. Vogelsang, and H. Bunzel (2000), “Simple Robust Testing of Regression
Hypotheses,” Econometrica, 69, 695-714.
Kiefer, N. and T.J. Vogelsang (2002), “"Heteroskedasticity-Autocorrelation Robust
Standard Errors Using the Bartlett Kernel Without Truncation," Econometrica, 70,
2093-2095, 2002
Müller, Ulrich (2007), “A Theory of Robust Long-Run Variance Estimation,” Journal of
Econometrics, 141, 1331-1352.
*Newey, W.K. and K.D. West (1987), “A Simple Positive Semi-Definite,
Heteroskedasticity and Autocorrelation Consistent Covariance Matrix,”
Econometrica 55, 703-708.
Sun Y., P.C.B. Phillips, and S. Jin (2008), “Optimal Bandwidth Selection in
Heteroskedasticity-Autocorrelation Robust Testing,” Econometrica, 76(1): 175-194.

7. Generalized Method of Moments and Weak Instruments/Weak Identification

Andrews, D.W.K., M. Moreira, and J.H. Stock (2006). “Optimal Two-Sided Invariant
Similar Tests for Instrumental Variables Regression”, Econometrica 74, 715-752.
Andrews, D.W.K. and J.H. Stock (2007). “Inference with Weak Instruments,” in Advances
in Economics and Econometrics, Theory and Applications: Ninth World Congress of
the Econometric Society, Vol. III, ed. by R. Blundell, W. K. Newey, and T. Persson.
Cambridge, UK: Cambridge University Press.
Guggenberger, P. and R.J. Smith (2005), “Generalized Empirical Likelihood Estimators and
Tests under Partial, Weak and Strong Identification,” Econometric Theory 21, 667-
709.
*Hayashi, Ch. 3 and 4 or Hamilton, Ch. 14.
Hall, A.R., ch. 4-5

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Economics 2142 Fall 2009

*Hansen, L.P. and Singleton, K. (1982), “Generalized Instrumental Variable Estimation of

Nonlinear Rational Expectation Models,” Econometrica 1269-1286 and errata,
January 1984, 267-68.
*Hansen, L.P., J. Heaton, and A. Yaron (1996), “Finite Sample Properties of Some
Alternative GMM Estimators,” Journal of Business and Economic Statistics 14,
262-280.
Kleibergen, F.R. and S. Mavroeidis (2008), “Weak Instrument Robust Tests in GMM and
the New Keynesian Phillips Curve,” manuscript, Brown University.
*Newey, W.K. and D. McFadden (1994), “Large Sample Estimation and Hypothesis
Testing,” ch. 36 in R. Engle and D. McFadden (eds.), Handbook of Econometrics,
vol. IV, 2113-2247. Amsterdam: Elsevier.
Staiger, D. and J.H. Stock (1997), “Instrumental Variables Regression with Weak
Instruments,” Econometrica 65, no. 3, 557-586
Stock, J.H., M. Yogo, and J. Wright (2002), “A Survey of Weak Instruments and Weak
Identification in Generalized Method of Moments,” Journal of Business and
Economic Statistics, 20, 518 – 529.
*Stock, J.H. and J. Wright (2000), “GMM With Weak Identification,” Econometrica 68,
1055 – 1096.
Yogo, M. (2004), “Estimating the Elasticity of Intertemporal Substitution when the
Instruments are Weak,” Review of Economics and Statistics 86, 797-810.

8. The Kalman and NonGaussian filter and applications

8a. The Kalman and Non-Gaussian filter
Anderson, B.D.O. and J.B. Moore (2005), Optimal Filtering, Dover Publishing.
Harvey, Ch. 4; Ch. 5.1-5.4
*Hamilton, Ch. 22
Kitagawa, G. (1987), “Non-Gaussian State Space Modelling of Non-Stationary Time
Series,” with discussion, Journal of the American Statistical Association, 82, 1032-
1063.
8b. Linear Gaussian models with unobserved components
Müller, U.K. and P.E. Petalas (2008), “Efficient Estimation of the Parameter Path in
Unstable Time Series Models,” manuscript, Princeton University.
Stock, J.H. and M.W. Watson (1991), “A Probability Model of the Coincident Economic
Indicators,” in G. Moore and K. Lahiri, eds., The Leading Economic Indicators:
New Approaches and Forecasting Records, Cambridge: Cambridge University
Press, 63-90.
Stock, James H., and Mark W. Watson (1998), Asymptotically Median Unbiased
Estimation of Coefficient Variance in a Time Varying Parameter Model, Journal of
the American Statistical Association, Vol. 93, No. 441, March 1998, pp. 349-358.
8c. Regime switching
*Hamilton, J.D. (1989), “A New Approach to the Economic Analysis of Nonstationary
Time Series and the Business Cycle,” Econometrica 57, 357-384.
Pesaran, H., D. Pettenuzzo, and A. Timmerman (2006), “Forecasting Time Series Subject to
Multiple Structural Breaks.” Review of Economic Studies, 73(1), 1057-1084.
Smith, A. (2008), “Markov Breaks in Regression Models,” manuscript, UCS

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Economics 2142 Fall 2009

9. Asymptotics II: Beveridge-Nelson decomposition, short-cuts to time series asymptotics and

convergence to stochastic integrals
*Beveridge, S. and Nelson, C. R. (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, 151-174.
*Hamilton, Ch. 17.
Hall and Heyde, Chs. 3, 4, and 5 and the Appendix.
Ibragimov, R. and Phillips, P. C. B. (2008). Regression asymptotics using martingale
convergence methods. Econometric Theory 28 (2008), 1-60.
Jacod, J. and Shiryaev, A. N. (2003). Limit theorems for stochastic processes. 2nd edition.
Springer-Verlag, Berlin. Chs. I, III, VI, and IX.
* Phillips, P.C.B. and Solo, V. (1992). Asymptotics for Linear Processes. Annals of
Statistics 20, 971-1001.
Prigent, J.-L. (2003). Weak convergence of financial markets. Berlin: Springer-Verlag.
Sections 1.1-1.4, 3.1 and 3.3.
*Stock, J. H. (1994). Unit roots and trend breaks in econometrics. Handbook of
Econometrics, Vol. IV, 2740-2841 (sections 1-4).

10. Modeling of and inference for persistent time series

10a. Univariate unit roots: estimation, testing, and local to unity theory
Dickey, D.A., and W.A. Fuller (1979), “Distribution of the Estimators for Autoregressive
Time Series With a Unit Root,” Journal of the American Statistical Association 74,
no. 366, 427-431.
Elliott, G., T.J. Rothenberg, and J.H. Stock (1996), “Efficient Tests for an Autoregressive
Unit Root,” Econometrica 64, 813-836.
Haldrup, N. and M. Jansson (2006), “Improving Size and Power in Unit Root Testing,” in
Palgrave Handbook of Econometrics, Volume 1: Econometric Theory, 252-277.
Mikusheva, A. (2007), “Uniform Inference in Autoregressive Models,” Econometrica 75,
1411-1452.
Nelson, C.R., and C.I. Plosser (1982), “Trends and Random Walks in Macroeconomic Time
Series,” Journal of Monetary Economics, 129-162.
Ng, S. and P. Perron (2001), “Lag Length Selection and the Construction of Unit Root Tests
with Good Size and Power,” Econometrica 6, 1519–1554.
Phillips, P.C.B. (1987), “Time Series Regression with Unit Roots”, Econometrica, 55, 277-
302.
Stock, J.H. (1991), “Confidence Intervals for the Largest Autoregressive Root in U.S.
Economic Time Series,” Journal of Monetary Economics 28, no. 3, 435-460.
*Stock, J.H. (1994), “Unit Roots and Trend Breaks,” Handbook of Econometrics, v. IV,
sections 1-4.

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Economics 2142 Fall 2009

10b. Multivariate unit roots and cointegration

Chan, N.H., and Wei, C.Z. (1988), “Limiting Distributions of Least Squares Estimates of
Unstable Autoregressive Processes,” Annals of Statistics 16, March 1988, 367-401.
Elliott, G. (1998), “The Robustness of Efficient Cointegration Estimators when Regressors
Almost Have Unit Roots,” Econometrica 66, 149-158.
*Engle, Robert F., and C.W.J. Granger (1987), “Co-Integration and Error Correction:
Representation, Estimation and Testing,” Econometrica 55, 251-276.
Haug, A.A. (1996), “Tests for Cointegration: A Monte Carlo Comparison,” Journal of
Econometrics 71.
Johansen, S. (1988a), “Statistical Analysis of Cointegration Vectors,” Journal of Economic
Dynamics and Control, 12, 231-255.
Phillips, P.C.B. and S. Ouliaris (1990), “Asymptotic Properties of Residual Based Tests for
Cointegration,” Econometrica, 58, 165-94.
Saikkonen, P. (1991), “Asymptotically Efficient Estimation of Cointegrating Regressions,”
Econometric Theory, 7, 1-21.
Sims, C.A., J.H. Stock, and M.W. Watson (1990), “Inference in Linear Time Series Models
with Some Unit Roots,” Econometrica 58, 113-144.
Stock, J.H. (1987), “Asymptotic Properties of Least Squares Estimators of Cointegrating
Vectors,” Econometrica 55, 1035-1056.
Stock, J.H. and M.W. Watson (1993), “A Simple Estimator of Cointegrating Vectors in
Higher-Order Integrated Systems”, Econometrica, 61 (1993), no. 4, 783-820.
*Watson, M.W. (1994), “Vector Autoregressions and Cointegration,” Handbook of
Econometrics, v. IV, 2844-2915 (sections 1 and 2).

10c. Predictive regression with persistent regressors

Cavanagh, C., G. Elliott, and J.H. Stock (1995), “Inference in Models with Nearly
Nonstationary Regressors,” Econometric Theory, 11 (1995)
Chen, W. and R. Deo (2008), “Bias Reduction and Likelihood Based Almost-Exactly Sized
Hypothesis Testing in Predictive Regressions Using the Restricted Likelihood,”
manuscript, Texas A&M University.
Jansson, M. and M. Moreira (2006), “Optimal Inference in Regression Models with Nearly
Integrated Regressors,” Econometrica, 74, 681-714.

10d. Long memory and fractional integration

Baillie, R. T. (1996). Long memory processes and fractional integration in econometrics.
Journal of Econometrics 73, 5-59.
Beran, J. (1994). Statistics for long-memory processes. New York, Chapman & Hall.
*Campbell, Lo and MacKinlay, Section 2.6.
Diebold, F. and Inoue, A. (2001). Long memory and regime switching. Journal of
Econometrics 105, 131-159.
Hosking, J. P. M. (1996). Asymptotic distributions of the sample mean, autocovariances,
and autocorrelation of long-memory time series. Journal of Econometrics 73, 261-
284.
*Lo, A. (1991). Long term memory in stock market prices. Econometrica 59, 1279-1313.

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Economics 2142 Fall 2009

*Phillips, P. C. B. (2007). Unit root log periodogram regression. Journal of Econometrics

138, 104-124.
Robinson, P. M. (Ed.) (2003). Time series with long memory. Oxford: Oxford University
Press.

11. Stochastic volatility and GARCH models

11a. GARCH processes and estimation
Bollerslev, T., Chou, R. Y. and Kroner, K. F. (1992). ARCH Modelling in finance: A
review of the theory and empirical evidence. Journal of Econometrics 52, 5-59.
Bollerslev T., Engle R. F. and Nelson D. B. (1994). ARCH model. In Handbook of
Econometrics 4, Engle R. F. and McFadden D. L. (eds). Elsevier Science: New
York; 2961–3031.
*Davis, R. A. and Mikosch, T. (1998). The sample autocorrelations of heavy-tailed
processes with applications to ARCH. Annals of Statistics 26, 2049-2080.
Engle R. F. (2001). GARCH 101: An introduction to the use of ARCH/GARCH models in
applied Econometrics. Journal of Economic Perspectives 15, 157-168.
* Engle, R. F. (2002). New frontiers for ARCH models. Journal of Applied Econometrics
17, 425-446.
Engle, R. F. (2004). Risk and volatility: Econometric models and financial practice.
American Economic Review 94, 405-420.
Hamilton (1994), Ch. 21.
*Mikosch, T. and Starica, C. (2000). Limit theory for the sample autocorrelations and
extremes of a GARCH(1, 1) process. Annals of Statistics 28, 1427--1451.
*Poon, S.-H. and Granger, C. W. J. (2003). Forecasting volatility in financial markets: A
review, Journal of Economic Literature 41, 478-539.

11b. Stochastic volatility models

*Aït-Sahalia, Y. and Kimmel, R. Maximum likelihood estimation of stochastic volatility
models. Journal of Financial Economics 83 (2007) 413–452. Available at
http://www.princeton.edu/~yacine/stochvol.pdf
Alizadeh, S., Brandt, M. W. and Diebold, F. X. (2002). Range-based estimation of
stochastic volatility models. Journal of Finance 57, 1047-1091.
*Andersen, T. G., Bollerslev and Diebold, F. X. (2002). Parametric and nonparametric
volatility measurement. In: Handbook of Financial Econometrics (Aït-Sahalia, Y.
and Hansen, L. P., Eds), Amsterdam: North Holland. Available at
http://home.uchicago.edu/~lhansen/abd_handbook_101304.pdf
Andersen, T. G., Bollerslev, T. Diebold, F. X. and Labys, P. (2003). Modeling and
forecasting realized volatility. Econometrica 71, 579-625.
*Barndorff-Nielsen, O. E. and Shephard, N. (2004). Econometric analysis of realized
covariation: High frequency based covariance, regression, and correlation in
financial economics. Econometrica 72, 885-925.
Barndorff-Nielsen, O. E. and Shephard, N. (2005). How accurate is the asymptotic
approximation to the distribution of realised volatility? in Identification and
Inference for Econometric Models. A Festschrift for Tom Rothenberg, (edited by
Donald W.K. Andrews and James H. Stock), Cambridge University Press, 2005,
306—331. Available at

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Economics 2142 Fall 2009

http://www.nuff.ox.ac.uk/economics/papers/2001/w16/tom.pdf
Broto, C. and Ruiz, E. (2004). Estimation methods for stochastic volatility models: A
survey. Journal of Economic Surveys 18, 613-649.
Eraker, B., Johannes, M. and Polson, N. (2003). The impact of jumps in volatility and
returns. Journal of Finance 58, 1269-1300.
*Kim, S., Shephard, N. and Chib, S. (1998). Stochastic volatility: Likelihood inference and
comparison with ARCH models. Review of Economic Studies 65, 361-393.
(Also Poon and Granger, 2003, in 11a).

12. Inference in continuous time models

12a. Introduction to continuous-time stochastic processes and stochastic calculus
Durrett, R. (1996). Stohastic calculus. A practical introduction. CRC Press, Boca Raton,
FL.
Karatzas, I. and Shreve, S. (1991). Brownian motion and stochastic calculus. Springer-
Verlag, New York.
Karatzas, I. (1997). Lectures on the Mathematics of Finance, American Math Soc.,
Providence, RI.
12b. Estimation procedures and applications
*Ait-Sahalia, Y. (2002). Telling from discrete data whether the underlying continuous-time
model is a diffusion. Journal of Finance 57, 2075-2112.
Ait-Sahalia, Y. (2002). Maximum-likelihood estimation of discretely-sampled diffusions: A
closed-form approximation approach. Econometrica 70, 223-262.
*Andersen, T. G., Bollerslev and Diebold, F. X. (2002). Parametric and nonparametric
volatility measurement. In: Handbook of Financial Econometrics (Aït-Sahalia, Y.
and Hansen, L. P., Eds), Amsterdam: North Holland. Available at
http://home.uchicago.edu/~lhansen/abd_handbook_101304.pdf
Andersen, T. G., Bollerslev, T. Diebold, F. X. and Labys, P. (2003). Modeling and
forecasting realized volatility. Econometrica 71, 579-625.
*Barndorff-Nielsen, O. E. and Shephard, N. (2004). Econometric analysis of realized
covariation: High frequency based covariance, regression, and correlation in
finamcial economics. Econometrica 72, 885-925.
Barndorff-Nielsen, O. E. and Shephard, N. (2005). How accurate is the asymptotic
approximation to the distribution of realised volatility? In: Identification and
Inference for Econometric Models. A Festschrift for Tom Rothenberg, (edited by D.
W.K. Andrews and J. H. Stock), Cambridge University Press, 2005, 306—331.
Available at http://www.nuff.ox.ac.uk/economics/papers/2001/w16/tom.pdf
*Bandi, F. M. and Phillips, P. C. B. (2002). Nonstationary continuous-time processes. In:
Handbook of Financial Econometrics (Aït-Sahalia, Y. and Hansen, L. P., Eds),
Amsterdam: North Holland. Available at
http://home.uchicago.edu/~lhansen/bandi.pdf
*Bates, D.S. (1996). Testing option pricing models. In: Maddala, G.S., Rao, R. (Eds.),
Handbook of Statistics 14, Elsevier, Amsterdam, 567–611.
*Campbell, Lo and MacKinlay, Sections 9.1, 9.2, 9.3.
Lo, A. W. (1988). Maximum likelihood estimation of generalized Ito processes with
discretely sampled data. Econometric Theory 4, 231-524.

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Economics 2142 Fall 2009

13. Vector Autoregressions and SVARs

13a. Impulse response functions, variance decompositions, inference
*Lutkepohl, H., Introduction to Multiple Time Series Analysis, Second Edition. New York:
Springer-Verlag, 1993, ch. 3.7
*Sims, C.A. (1980), “Macroeconomics and Reality,” Econometrica 48, pp 1-48.
Stock, J.H. and M.W. Watson (2001) “Vector Autoregressions,” Journal of Economic
Perspectives 15 (Fall 2001), 101 – 116.
Watson, M.W. (1994), “Vector Autoregressions and Cointegration,” Handbook of
Econometrics, v. IV, 2844-2915 (section 3 only).
Wright, J.H. (2000), “Confidence Intervals for Univariate Impulse Responses with a Near
Unit Root,” Journal of Business and Economic Statistics 18, 368 – 373.

13b. Structural VARs: identification schemes

Bernanke, B., M. Gertler, and M. Watson (1997), “Systematic Monetary Policy and the
Effects of Oil Price Shocks,” Brookings Papers on Economic Activity 1997:1, 91-
158 (with discussion)
*Blanchard, O.J., and M.W. Watson, “Are Business Cycles All Alike?” in R.J. Gordon
(ed.), The American Business Cycle, University of Chicago Press: Chicago, 1986.
*Blanchard, O.J., and Quah, D. (1989), “Dynamic Effects of Aggregate Demand and
Supply Disturbances,” American Economic Review 79, 655-673.
Cochrane, J.H., and M. Piazzesi (2002). “The Fed and Interest Rates: A High-Frequency
Identification,” American Economic Review 92 (May), 90-95
Faust, J., Rogers, J.H., Swanson, E., and Wright, J.H. (2003). “Identifying the Effects of
Monetary Policy Shocks on Exchange Rates Using High Frequency Data,” Journal
of the European Economic Association 1(5), 1031-57.
Faust, J., E. Swanson, and J. Wright (2004). “Identifying VARs Based on High-Frequency
Futures Data.” Journal of Monetary Economics 51(6), 1107-31.
Gali, J. (1999). “Technology, Employment, and the Business Cycle: Do Technology Shocks
Explain Aggregate Fluctuations?” American Economic Review 89, 249-271.
King, Robert G., C.I. Plosser, J.H. Stock, and M.W. Watson (1991), “Stochastic Trends and
Economic Fluctuations,” American Economic Review 81, no. 4, 819-840.
Rigobon, R. (2003). “Identification through Heteroskedasticity,” The Review of Economics
and Statistics 85, 777-792.
Rigobon, R. and B. Sack (2004). “The impact of Monetary Policy on Asset Prices,” Journal
of Monetary Economics 51, 1553-1575.
Rudebusch, G.D. (1998), “Do Measures of Monetary Policy in a VAR Make Sense?”
International Economic Review, 39, 907 – 931.
Uhlig, H. (2005). “What are the effects of monetary policy on output? Results from an
agnostic identification procedure.” Journal of Monetary Economics 52, 381–419.

13c. Inference with long-run restrictions

Chari, V.V., P.J. Kehoe, and E. McGrattan (2007), “A Critique of Structural VARs Using
Real Business Cycle Theory” (aka “Are Structural VARs with Long-Run
Restrictions Useful in Developing Business Cycle Theory?”) Federal Reserve Bank
of Minneapolis Working Paper Series 634.

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Economics 2142 Fall 2009

Cooley, T. and M. Dwyer (1998). “Business Cycle Analysis without Much Theory: A Look
at Structural VARs,” Journal of Econometrics 83, 57-88.
Gali, J. (1999). “Technology, Employment, and the Business Cycle: Do Technology Shocks
Explain Aggregate Fluctuations?” American Economic Review 89, 249-271.
Gospodinov, N. (2008), “Inference in Nearly Nonstationary SVAR Models with Long-Run
Identifying Restrictions,” Journal of Business and Economic Statistics, forthcoming.
Pagan, A.R. and J.C. Robertson (1998). “Structural Models of the Liquidity Effect,” The
Review of Economics and Statistics 80, 202-217.
Watson, M.W. (2006), “Comment on Christiano, Eichenbaum, and Vigfusson’s ‘Assessing
Structural VARs’,” NBER Macroeconomics Annual 2006, 97-102.

13d. Inference for impulse responses

Kilian, L. (2001). “Impulse Response Analysis in Vector Autoregressions with Unknown
Lag Order”, Journal of Forecasting 20, 161-179.
Kilian, L. and P.-L. Chang (2000). “How Accurate are Confidence Intervals for Impulse
Responses in Large VAR Models?,” Economics Letters 69, 299-307.
Sims, C.A. and T. Zha (1999), “Error Bands for Impulse Responses,” Econometrica 1113-
1155.

14. Estimation and inference of linearized DSGEs

Canova, F. and L. Sala (2006), “Back to Square One: Identification Issues in DSGE
Models,” manuscript, CREI.
*DeJong and Dave, ch.2-4
Ireland, P.N. (2000), “Sticky-Price Models of the Business Cycle: Specification and
Stability,” Journal of Monetary Economics 47, 3-18.
Sargent, T.J. (1989). “Two Models of Measurements and the Investment Accelerator,”
Journal of Political Economy 97, 251-287.
Smets, F. and R. Wouters (2003), “An Estimated Dynamic Stochastic General Equilibrium
Model of the Euro Area,” Journal of the European Economic Association 1, 1123-
1175.

15. Large data sets: Dynamic Factor Models and FAVAR

Amengual, D. and M.W. Watson (2007). “Consistent Estimation of the Number of Dynamic
Factors in a Large N and T Panel,” Journal of Business and Economic Statistics, 91-
96.
Aruoba, S.B., F.X. Diebold, and C. Scotti (2008), “Real-Time Measurement of Business
Conditions,” NBER WP 14349
Bai, J., and S. Ng (2002), “Determining the number of factors in approximate factor
models”, Econometrica 70:191-221.
Bai, J. and S. Ng (2007b), “Instrumental Variable Estimation in a Data-Rich Environment,”
manuscript, University of Michigan.
Bai, J., and S. Ng (2007a), “Determining the number of primitive shocks in factor models”,
Journal of Business and Economic Statistics 25:52-60.
Bernanke, B.S., J. Boivin and P. Eliasz (2005). “Measuring the effects of monetary policy: a
factor-augmented vector autoregressive (FAVAR) approach”, Quarterly Journal of
Economics 120: 387–422.

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Boivin, J. and M.P. Giannoni (2006). “DSGE Models in a Data-Rich Environment,” NBER
WP12772.
Boivin, Jean and Serena Ng (2005). “Understanding and Comparing Factor-Based
Forecasts,” International Journal of Central Banking 1, 117-151.
Doz, C., D. Giannone, and L. Reichlin (2006), “A Quasi Maximum Likelihood Approach
for Large Approximate Dynamic Factor Models,” ECB Working Paper 674.
Forni, M., and L. Reichlin (1998), “Let’s get real: a dynamic factor analytical approach to
disaggregated business cycle”, Review of Economic Studies 65:453-474.
Forni, M., M. Hallin, M. Lippi and L. Reichlin (2005), “The generalized dynamic factor
model: one-sided estimation and forecasting”, Journal of the American Statistical
Association 100, 830-839.
Geweke, J. (1977), “The Dynamic Factor Analysis of Economic Time Series”, in: D.J.
Aigner and A.S. Goldberger, eds., Latent Variables in Socio-Economic Models,
(North-Holland, Amsterdam).
Kapetanios, G. and M. Marcellino (2008). “Factor-GMM Estimation with Large Sets of
Possibly Weak Instruments,” manuscript, EUI
Onatski, A. (2008), “Testing Hypotheses about the Number of Factors in Large Factor
Models,” manuscript, Columbia University.
Reiss, R. and M.W. Watson (2007). “Relative Goods’ Prices and Pure Inflation,”
manuscript, Princeton University.
Sargent, T.J., and C.A. Sims (1977), “Business cycle modeling without pretending to have
too much a-priori economic theory”, in: C. Sims et al., eds., New Methods in
Business Cycle Research (Federal Reserve Bank of Minneapolis, Minneapolis).
Stock, J.H., and M.W. Watson (2002a). “Forecasting Using Principal Components from a
Large Number of Predictors,” Journal of the American Statistical Association
97:1167–1179.
*Stock, J.H. and M.W. Watson (2006a), “Forecasting with many predictors,” Ch. 6 in
Graham Elliott, Clive W.J. Granger and Allan Timmermann (eds.), Handbook of
Economic Forecasting, Elsevier, 515-554.
Timmermann, A. (2006), “Forecast Combinations,” in G. Elliott, C.W.J. Granger, and A.
Timmerman (eds), Handbook of Economic Forecasting, Vol. 1, Elsevier.

16. Model evaluation and forecast comparison

Clark, T. and M. McCracken (2001),” Tests of Equal Forecast Accuracy and Encompassing
for Nested Models,” Journal of Econometrics, 105, 85-110.
Clark, T. and K. West (2006), “Using Out-of-Sample Mean Squared Prediction Errors to
Test the Martingale Difference Hypothesis,”Journal of Econometrics 135(1-2), 155-
186.
Diebold, F.X., T.A. Gunther, and A.S. Tay (1998), “Evaluating Density Forecasts with
Applications to Financial Risk Management,” International Economic Review,
39(4), 863-883.
Faust, J. and J. Wright (2008), “Efficient Predictive Regressions,” manuscript, Johns
Hopkins University
Giacomini, R. and H. White (2006), “Tests of Conditional Predictive Ability,”
Econometrica, 74(6), 1545-1578

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Hansen, P.R. (2008), “In-Sample and Out-of-Sample Fit: Their Joint Distribution and its
Implications for Model Selection,” manuscript, Stanford University
McCracken, M. (2000), “Robust Out of Sample Inference,” Journal of Econometrics, 99,
195-223.
*West, K.D. (1996), “Asymptotic Inference about Predictive Ability,” Econometrica, 64,
1067-1084.
*West, K.D. (2006), “Forecast Evaluation,” 100-134 in Handbook of Economic
Forecasting, Vol. 1, G. Elliott, C. Granger and A. Timmerman (eds), Amsterdam:
Elsevier.

17. Inference in heavy-tailed time series and robustness

17a. Stylized facts and empirical properties of financial time series. Implications for
economic decisions
*Cont, R. (2001). Empirical properties of asset returns: stylized facts and statistical issues.
Quantitative Finance 1, 223-236. Available at http://www-
tat.wharton.upenn.edu/~steele/Resources/FTSResources/StylizedFacts/Cont2001.pdf
Gabaix, X., Gopikrishnan, P., Plerou, V. and Stanley, H. E. (2003). A theory of power-law
distributions in financial market fluctuations. Nature 423, 267-270.
Ibragimov, R. (2009). Heavy-tailed densities. The New Palgrave Dictionary of Economics
Online. Eds. Steven N. Durlauf and Lawrence E. Blume. Palgrave Macmillan, 2009.
Loretan, M. and Phillips, P. C. B. (1994). Testing the covariance stationarity of heavy-tailed
time series. Journal of Empirical Finance 1, 211-248. Available at
http://cowles.econ.yale.edu/P/cp/p08b/p0866.pdf

17b. Asymptotics and tail index estimation

*Davis, R. A. and Mikosch, T. (1998). The sample autocorrelations of heavy-tailed
processes with applications to ARCH. Annals of Statistics 26, 2049-2080.
Gabaix, X. and Ibragimov, R. (2006). LOG(RANK-1/2): A simple way to improve the OLS
estimation of tail exponents. Forthcoming in the Journal of Business & Economic
Statistics. Harvard Institute of Economic Research Discussion Paper No. 2106.
http://www.economics.harvard.edu/faculty/ibragimov/files/GabaixIbragimovFin.pdf
Hill, B. M. (1975). Simple general approach to inference about tail of a distribution. Annals
of Statistics 3, 1163-1174.
Huisman, R., Koedijk, K. G. , Kool, C. J. M. and Palm, F. (2001). Tail-index estimates in
small samples. Journal of Business & Economic Statistics 19, 208-216.
Loretan, M. and Phillips, P. C. B. (1994). Opt. cit.
McCulloch, J. H. (1997). Measuring tail thickness to estimate the stable index alpha: A
critique. Journal of Business and Economic Statistics 15, 74-81.
Mikosch, T. and Starica, C. (2000). Limit theory for the sample autocorrelations and
extremes of a GARCH(1, 1) process. Annals of Statistics 28, 1427--1451.
Quintos, C., Fan Z. H. and Phillips, P. C. B. (2001). Structural change tests in tail behaviour
and the Asian crisis. Review of Economic Studies 68, 633-663.
Silverberg, G. and Verspagen, B. (2007). The size distribution of innovations revisited: An
application of extreme value statistics to citation and value measures of patent
significance. Journal of Econometrics 2, 318-339.

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18. Copulae and dependence modeling for time series and Markov processes
*Chen, X. and Y. Fan (2006). Estimation of copula-based semiparametric time series
models. Journal of Econometrics 130, 307{335.
Darsow, W. F., Nguyen, B. and Olsen, E. T. (1992). Copulas and Markov processes. Illinois
Journal of Mathematics 36, 600{642.
Ibragimov, R. (2009). Copula-based characterizations for higher-order Markov processes.
Econometric Theory 25, 819-846.
*McNeil, A. J., Frey, R. and Embrechts, P. (2005). Quantitative risk management.
Concepts, techniques and tools. Princeton University Press, Princeton, NJ.
Nelsen, R. B. (1999). An introduction to copulas. Lecture Notes in Statistics, 139. Springer-
Verlag, New York, 216 pp.
*Patton, A. (2006). Modelling asymmetric exchange rate dependence. International
Economic Review 47, 527{556.

19. Introduction to Markov Chain Monte Carlo (MCMC) methods in econometrics

Chib, S. and E. Greenberg (1996), “Markov Chain Monte Carlo Simulation Methods in
Econometrics,” Econometric Theory 12, 409-431.
Chib, C., N. Nardari, and N. Shephard (2002), “Markov Chain Monte Carlo Methods for
Stochastic Volatility Models,” Journal of Econometrics, 108, 281-316.
Durbin, J. and S.J. Koopman (1997), “Monte Carlo Maximum Likelihood Estimation for
Non-Gaussian State Space Models,” Biometrika.
*Geweke, John (2005), Contemporary Bayesian Econometrics and Statistics, New York:
Wiley, ch. 4
Harvey, A.C., E. Ruiz and N. Shephard (1994), “Multivariate Stochastic Variance Models,”
Review of Economic Studies, 61, 247-264.
Kim, C.-J. and C.R. Nelson (1998), “Business Cycle Turning Points, a New Coincident
Index, and Tests of Duration Dependence Based on a Dynamic Factor Model with
Regime-Switching,” The Review of Economics and Statistics, 188-201.
Kim, S., N. Shephard, and S. Chib (1998), “Stochastic Volatility, Likelihood Inference, and
Comparison with ARCH models,” Review of Economic Studies, 361-394.
Kitagawa, G. (1996), “Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State
Space Models,” Journal of Computational and Graphical Statistics, 5, 1-25.
Pitt, M.K. and N. Shephard (1999), “Filtering via Simulation: Auxiliarly Particle Filters,”
Journal of the American Statistical Association, 94(446), 590-599.

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