Course Objective

The course will cover some advanced topics in time series econometrics and forecasting.
We will cover theory, methods, and applications. The primary emphasis will be on methods, with theory presented as an aid to understanding the methods. All methods will be carefully illustrated in full detail by applications to macroeconomic aggregates including quarterly GDP and monthly unemployment rates.

Day 1: Forecasting

The first lecture will focus on forecasting from semiparametric linear models. We will first discuss one-step-ahead forecasts, including point forecasts, interval forecasts and density forecasts. We will then move on to multi-step-ahead forecasts, including both iterated one-step forecasts and direct forecasts. Fan charts will be introduced. The forecast methods will be fully general and not rely on distributional assumptions.

Day 2: Structural Breaks

The second lecture will deal with the econometrics of structural breaks. Breaks in the mean, variance and coefficients will be introduced. One-time breaks, multiple breaks and smooth structural change will be discussed. Methods to test for the presence of breaks will be introduced, including tests for single structural breaks and tests for multiple breaks. Estimation and confidence intervals for breaks will be introduced, including single and multiple breaks.

Day 3: Nonlinear Time Series

The third lecture will focus on nonlinear time series models, in particular the threshold autoregressive (TAR) model. Formulating nonlinear models, estimation of nonlinear models, and tests for nonlinearity and threshold effects will be discussed. Forecasting from nonlinear models will also be addressed.

Day 4: Model and Forecast Selection

The fourth lecture will introduce methods for selection of time series models. Information criterion (AIC, BIC, PLS, cross-validation) will be derived and compared. The theory of model selection will be developed based on minimizing mean-squared error and mean-squared forecast error.

Day 5: Model and Forecast Combination

The final lecture will introduce methods for model and forecast combination. Traditional methods, including Bates-Granger weights and Granger-Ramanathan weights will be reviewed. Modern methods including Bayesian model averaging and AIC weights will be introduced. Current methods including Forecast model averaging and leave-h-out cross validation will be covered. The theory of forecast combination will be developed based on minimization of mean-square forecast error, and information criterion as estimates of MSFE. Forecast combination methods will be present for both one-step and multi-step forecasts, for point forecasts and for forecast intervals and densities.

Practical Lab Sessions

The afternoon sessions will be devoted to empirical exercises. Students will estimate time-series models on real data, make forecasts, forecast intervals, and implement model selection and combination methods.

Reading List

Forecasting

Massimiliano Marcellino, James Stock, and Mark Watson (2006): “A comparison of direct and iterated multistep AR methods for forecasting macroeconomic series,” Journal of Econometrics, 135, 499-526,pdf

Handbook of Economic Forecasting (2006) link

C.W.J. Granger, H. White and M. Kamstra: “Interval Forecasting: An Analysis Based Upon ARCH-Quantile Estimators,” Journal of Econometrics, 40, 87-96 (1989). pdf

Structural Change

Donald Andrews (1993): “Tests for parameter instability and structural change with unknown change point,” Econometrica, 61, 821-856. pdf

Jushan Bai (1997) “Estimation of a change point in multiple regression models,” Review of Economics and Statistics, 79, 551-563. pdf

Jushan Bai and Pierre Perron (1998): “Estimating and testing linear models with multiple structural changes,” Econometrica, 66, 47-78. pdf

Margaret McConnell and Gabriel Pérez-Quirós (2000): “Output fluctuations in the United States: what has changed since the early 1980s?”, American Economic Review, 90, 1464-1476. pdf

Bruce E. Hansen (2000): “Testing for structural change in conditional models,” Journal of Econometrics, 97, 93-115. pdf

Bruce E. Hansen (2001): “The New Econometrics of Structural Change: Dating Changes in U.S. Labor Productivity.” Journal of Economic Perspectives, 15, 117-128. pdf

Donald Andrews (2003): “End-of-Sample Instability Tests,” Econometrica, 71, 1661-1694. pdf

M. Hashem Pesaran and Allan Timmermann (2007): “Selection of estimation window in the presence of breaks,” Journal of Econometrics, 137, 134-161. pdf

Graham Elliott and Ulrich Muller (2007): “Confidence sets for the date of a single break in linear time series regression,” Journal of Econometrics, 141, 1196-1218 pdf

Nonlinear Time Series

Bruce E. Hansen (1996) “Inference when a nuisance parameter is not identified under the null hypothesis,” Econometrica. pdf

Jianqing Fan, Qiwei Yao and Howell Tong (1996) “Estimation of conditional densities and selectivity measures in dynamical systems,” Biometrika, 83, 189-206, pdf

Bruce E. Hansen (1997) “Inference in TAR models,” Studies in Nonlinear Dynamics and Econometrics. pdf

Jianqing Fan and Qiwei Yao (1998): “Efficient estimation of conditional variance functions in stochastic regression,” Biometrika, 85, 645-660, pdf

Peter Hall, R.C.L. Wolff and Qiwei Yao (1999) “Methods for estimating a conditional distribution function” JASA, 94, 154-163, pdf

Bruce E. Hansen (1999) “Testing for linearity,” Journal of Economic Surveys. pdf

Bruce E. Hansen (2000) “Sample Splitting and Threshold Estimation” Econometrica pdf

Bruce E. Hansen and Mehmet Caner (2001): Threshold autoregression with a unit root,” Econometrica, 69, 1555-1596, pdf

Bruce E. Hansen and Byeongseon Seo (2002) “Testing for two-regime cointegration in vector error correction models,” Journal of Econometrics, 110, 293-318, pdf

Jianqing Fan and Qiwei Yao (2003) Nonlinear Time Series: Nonparametric and Parametric Methods.

Bruce E. Hansen (2011) “Threshold autoregression in economics,” Statistics and its Inferface, 4, 123-127, pdf

Nonparametrics

Jianqing Fan, Qiwei Yao and Howell Tong (1996) “Estimation of conditional densities and selectivity measures in dynamical systems,” Biometrika, 83, 189-206, pdf

Jianqing Fan and Qiwei Yao (1998): “Efficient estimation of conditional variance functions in stochastic regression,” Biometrika, 85, 645-660, pdf

Peter Hall, R.C.L. Wolff and Qiwei Yao (1999) “Methods for estimating a conditional distribution function” JASA, 94, 154-163, pdf

Jianqing Fan and Qiwei Yao (2003) Nonlinear Time Series: Nonparametric and Parametric Methods.

GMM and the Bootstrap

Hall and Horowtiz (1996) “Bootstrap critical values for tests based on generalized-method-of-moments estimation, Econometrica, 64, 891-916 pdf

Bruce E. Hansen (1999) “The grid bootstrap and the autoregressive model” Review of Economics and Statistics, 81, 594-607, pdf

Donald Andrews (2002) “Higher-order improvements of a computationally attractive k-step bootstrap for extremum estimators,” Econometrica, 70, 119-162. pdf

Alastair Hall and Atsushi Inoue (2003) “The large sample behavior of the generalized method of moments estimator in misspecified models,” Journal of Econometrics, 114, 361-394. pdf

Silvia Goncalves and Lutz Kilian (2004) “Bootstapping autoregressions with conditional heteroskedasticity of unknown form” Journal of Econometrics, 123, 89-120. pdf

Silvia Goncalves and Halbert White (2004) “Maximum likelihood and the bootstrap for nonlinear dynamic models,” Journal of Econometrics, 119, 199-219, pdf

Atsushi Inoue and Mototsugu Shintani (2006) “Bootstrapping GMM estimators for time series,” Journal of Econometrics, 133, 531-555. pdf

Anna Mikusheva (2007) Uniform inference in autoregressive models” Econometrica, 75, 1411-1452. pdf

Selection and Combination

Bruce E. Hansen (2007): “Least Squares Model Averaging.” Econometrica 75, 1175-1189. pdf

Bruce E. Hansen (2008): “Least Squares Forecast Averaging.” Journal of Econometrics 146, 342-350. pdf

Bruce E. Hansen: “Multi-step forecast selection” pdf

Bruce E. Hansen (2009): “Averaging Estimators for Regressions with a Possible Structural Break,” Econometric Theory, 35, 1498-1514. pdf

Bruce E. Hansen (2010): “Averaging Estimators for Autoregressions with a Near Unit Root,” Journal of Econometrics, 158, 142-155. pdf

Bruce E. Hansen and Jeffrey Racine (2012) “Jackknife Model Averaging” Journal of Econometrics, 167, 38-456. pdf