Economics 275: Time Series Analysis Professor Peter Hansen Spring 2011 Lectures: Mondays and Wednesdays: 13:1515:05 in McCullough 122. O¢ ce: Landau 229. O¢ ce Hours: Tuesday 10:00-11:00. Email: [email protected]. Course Description: The course will cover econometric topics of time series analysis. First, we discuss station- arity, ergodicity, and mixing that are important concepts for dependent processes and we establish law of large numbers and central limit theorems in this context. Second, we study maximum likelihood estimation (MLE) and quasi maximum likelihood estimation (QMLE) in the context of time-series, where the latter motivates robust covariance estimation. Third, we analyze autoregressive and moving average process, their multivariate extensions, and unit roots and cointegration in this framework. Forth, we review some issues related to fore- cast evaluation and comparisons. Fifth, an introduction to the recent literature on volatility models and volatility estimation based on high-frequency data. Required Textbook: (H) Hamilton (1994): Time Series Analysis, Princeton University Press. Other useful textbooks include: Davidson (1994): Stochastic Limit Theory, Oxford University Press; Davidson (2000): Econometric Theory, Blackwell Publishers; Johansen (1996): Likelihood-Based Inference in Cointegrated VAR Models, Oxford Uni- versity Press; White (1994): Estimation, Inference and Specication Analysis, Cambridge University Press; White (2000a): Asymptotic Theory for Econometricians, Academic Press. Grading: Will be based on: Problem sets (40%); In-class presentation and active partici- pation (20%); Empirical time series project (of your choice) (40%); Problem Sets: Solutions must be your own, but you are allowed and encouraged to work together, in particular on problems that involve computer simulations. The computer simulations are meant to improve your understanding of the theoretical re- sults and their limitations. The simulations will require knowledge of matrix oriented packages, such as: Gauss, Matlab, or Ox.1 Empirical Problem: The last problem set is an empirical project, where you are to apply time series methods to a data set of your choice. Active Class Participation: Requires you to have read the material before lectures and be active during classes. Course Homepage: See Stanford Coursework. . 1Ox Console can be downloaded for free at: doornik/download.html 1 Course Outline: 1. Stochastic Processes in Discrete Time. H:Ch.7 (a) Stationarity, Ergodicity, and LLN for Dependent Processes. (b) Mixing and CLTs for dependent variables. 2. Maximum Likelihood Estimation (MLE) and Quasi-MLE (QMLE). (a) Heteroskedasticity and Autocorrelation Consistent (HAC) Estimators. White (1980, 1982), Newey & West (1987), Andrews (1991), Kiefer & Vogelsang (2004). 3. Univariate Times Series (stationary). H:Ch.3 (a) Autoregressive processes (AR). (b) Moving average processes (MA). (c) Autoregressive moving average processes (ARMA). 4. Multivariate Time Series. H:Ch.11 (a) Vector autoregressive processes (VAR). Sims (1980), Stock & Watson (2001). 5. Unit Roots and Cointegration. H:Ch.17-19 (a) Univariate. Stock (1994). (b) Multivariate. Engle & Granger (1987), Johansen (1991), Watson (1994). (c) Grangers representation theorem. Hansen (2005a) (d) Structural changes and unit roots. Perron (1989, 1990). 6. Forecasting. (a) Combination: Bates & Granger (1969). (b) Macro forecasting: Stock & Watson (1999), Stock & Watson (2002a), Stock & Watson (2002b) (c) Comparisons: Diebold & Mariano (1995), West (1996), White (2000b), Hansen (2005b), Hansen, Lunde & Nason (2011), West (2005). 7. Volatility Models and Realized Variance (RV). H:Ch.21 (a) ARCH/GARCH. Engle (1982), Bollerslev (1986). (b) RV Dened and used for Prediction. Andersen & Bollerslev (1998), Andersen, Bollerslev & Meddahi (2004). (c) RV Distribution/Accuracy. Andersen, Bollerslev, Diebold & Labys (2000), An- dersen, Bollerslev, Diebold & Ebens (2001), Andersen, Bollerslev, Diebold & Labys (2001), Barndor¤-Nielsen & Shephard (2002). (d) Macro Applications. Andersen, Bollerslev, Diebold & Vega (2003). (e) RV and Market Microstructure Noise. Hansen & Lunde (2006), Barndor¤-Nielsen, Hansen, Lunde & Shephard (2006). (f) Realized GARCH. Hansen, Huang & Shek (2010). 2 References Andersen, T. G. & Bollerslev, T. (1998), Answering the skeptics: Yes, standard volatility models do provide accurate forecasts, International Economic Review 39(4), 885905. Andersen, T. G., Bollerslev, T., Diebold, F. X. & Ebens, H. (2001), The distribution of realized stock return volatility, Journal of Financial Economics 61(1), 4376. Andersen, T. G., Bollerslev, T., Diebold, F. X. & Labys, P. (2000), Exchange rate return standardized by realized volatility are (nearly) Gaussian, Multinational Finance Jour- nal 4(3&4), 159179. Andersen, T. G., Bollerslev, T., Diebold, F. X. & Labys, P. (2001), The distribution of exchange rate volatility, Journal of the American Statistical Association 96(453), 42 55. Correction published in 2003, volume 98, page 501. Andersen, T. G., Bollerslev, T., Diebold, F. X. & Vega, C. (2003), Micro e¤ects of macro announcements: Real-time price discovery in foreign exchange, American Economic Review 93(1), 3862. Andersen, T. G., Bollerslev, T. & Meddahi, N. (2004), Analytic evaluation of volatility forecasts, International Economic Review 45, 10791110. Andrews, D. W. K. (1991), Heteroskedasticity and autocorrelation consistent covariance matrix estimation, Econometrica 59, 817858. Barndor¤-Nielsen, O. E., Hansen, P. R., Lunde, A. & Shephard, N. (2006), Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise. Unpublished manuscript. Barndor¤-Nielsen, O. E. & Shephard, N. (2002), Econometric analysis of realised volatility and its use in estimating stochastic volatility models, Journal of the Royal Statistical Society B 64, 253280. Bates, J. M. & Granger, C. W. J. (1969), The combination of forecasts, Operational Re- search Quarterly 20, 451468. Bollerslev, T. (1986), Generalized autoregressive heteroskedasticity, Journal of Economet- rics 31, 307327. Davidson, J. (1994), Stochastic Limit Theory, Oxford University Press, Oxford. Davidson, J. (2000), Econometric Theory, Blackwell, Oxford. Diebold, F. X. &Mariano, R. S. (1995), Comparing predictive accuracy, Journal of Business and Economic Statistics 13, 253263. Engle, R. F. (1982), Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. ination, Econometrica 45, 9871007. Engle, R. F. & Granger, C. W. J. (1987), Co-integration and error correction: Representa- tion, estimation and testing, Econometrica 55, 251276. Hamilton, J. D. (1994), Time Series Analysis, Princeton University Press, Princeton N.J. Hansen, P. R. (2005a), Grangers representation theorem: A closed-form expression for I(1) processes, Econometrics Journal 8, 2338. Hansen, P. R. (2005b), A test for superior predictive ability, Journal of Business and Economic Statistics 23, 365380. Hansen, P. R., Huang, Z. & Shek, H. (2010), Realized garch: A joint model of returns and realized measures of volatility, forthcoming in Journal of Applied Econometrics . 3 Hansen, P. R. & Lunde, A. (2006), Realized variance and market microstructure noise, Journal of Business and Economic Statistics 24, 127218. The 2005 Invited Address with Comments and Rejoinder. Hansen, P. R., Lunde, A. & Nason, J. M. (2011), The model condence set, Econometrica 79, 456497. Johansen, S. (1991), Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models, Econometrica 59, 15511580. Johansen, S. (1996), Likelihood Based Inference in Cointegrated Vector Autoregressive Mod- els, 2nd edn, Oxford University Press, Oxford. Kiefer, N. & Vogelsang, T. (2004), A new asymptotic theory for heteroskedasticity- autocorrelation robust tests, Working paper . Newey, W. & West, K. (1987), A simple positive semi-denite, heteroskedasticity and auto- correlation consistent covariance matrix, Econometrica 55, 703708. Perron, P. (1989), The great crash, the oil price shock, and the unit root hypothesis, Econometrica 57, 13611401. Perron, P. (1990), Testing for a unit root in a time series with a changing mean, Journal of Business and Economic Statistics 8, 153162. Sims, C. A. (1980), Macroeconomics and reality, Econometrica 48, 148. Stock, J. H. (1994), Unit root, structural breaks and trends, in R. F. Engle & D. L. McFad- den, eds, Handbook of Econometrics, Vol. 5, North-Holland, chapter 46. Stock, J. H. &Watson, M. W. (1999), Forecasting ination, Journal of Monetary Economics 44, 293335. Stock, J. H. & Watson, M. W. (2001), Vector autoregressions, Journal of Economic Per- spectives 15, 101115. Stock, J. H. & Watson, M. W. (2002a), Forecasting using principal components from a large number of predictors, Journal of the American Statistical Association 97, 11671179. Stock, J. H. & Watson, M. W. (2002b), Macroeconomic forecasting using di¤usion indexes, Journal of Business and Economic Statistics 20, 147162. Watson, M. W. (1994), Vector autoregressions and cointegration, in R. F. Engle & D. L. McFadden, eds, Handbook of Econometrics, Vol. 5, North-Holland, chapter 47. West, K. D. (1996), Asymptotic inference about predictive ability, Econometrica 64, 1067 1084. West, K. D. (2005), Forecast evaluation, Working Paper . White, H. (1980), A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity, Econometrica 48, 817838. White, H. (1982), Maximum likelihood estimation of misspecied models, Econometrica 50, 125. White, H. (1994), Estimation, Inference and Specication Analysis, Cambridge University Press, Cambridge. White, H. (2000a), Asymptotic Theory for Econometricians, revised edn, Academic Press, San Diego. White, H. (2000b), A reality check for data snooping, Econometrica 68, 10971126. 4
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