# Topics in Time Series Analysis

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1 Topics in Time Series Analysis Massimiliano Marcellino EUI and Bocconi University This course reviews some recent developments in the analysis of time series data in economics, with a special emphasis on their use for forecasting and macroeconomic applications. The focus will be both on the theoretical underpinnings of the techniques and on their empirical implementation. The techniques will be illustrated with several empirical applications, mostly implemented in Gauss or Matlab. Students can use any other programming software. The final grade will be given by an average of the grades in three assignments (75%) and final exam (25%). The assignments will contain mostly empirical questions, the final exam mostly theoretical questions. The topics that will be covered include: 1. Review of linear models a) Review of the three approaches to analyze stationary processes: the Wold Theorem, the Autocovariance function, the Spectrum b) Review of estimation and inference for stationary and non-stationary processes c) Model selection by information criteria d) Forecasting e) Example: AR vs Leading indicator forecasts for euro area GDP and inflation (Forecast robustness) f) Example: Country specific vs euro area forecasts for euro area IP, inflation and unemployment (Forecasting the aggregate vs aggregating the forecasts) g) Example: h-step ahead forecasts for US macro variables (Multi-step estimation vs iterated formulae for h-step ahead forecasting) h) Example: path confidence regions (measures of forecast uncertainty) Hamilton, J.D., (1994), Time Series Analysis, Princeton: Princeton University Press. (Ch. 3, 4, 6 and 10) Clements, M.P. and D.F. Hendry (1998). Forecasting Economic Time Series. Cambridge: Cambridge University Press (Ch. 6 and 11). Banerjee, A. N., Marcellino, M., and I. Masten (2005), "Leading indicators for Euro area inflation and GDP growth", Oxford Bulletin of Economics and Statistics, 67, Jorda, O. (2005), "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, 95, Jorda, O., Knuppel, M., Marcellino, M. (2010) Empirical Simultaneous Confidence Regions for Path-Forecasts, Bundesbank WP 2010/6.

2 Marcellino, M., Stock, J.H. and Watson, M.W. (2003), Macroeconomic Forecasting in the Euro Area: Country Specific Versus Euro Wide Information, European Economic Review, 47, pp Marcellino, M., Stock, J.H. and Watson, M.W. (2006), A Comparison of Direct and Iterated AR Methods for Forecasting Macroeconomic Series h-steps Ahead, Journal of Econometrics, 135, Watson, M.W. (2007), How Accurate Are Real-Time Estimates of Output Trends and Gaps?, Federal Reserve Bank of Richmond Economic Quarterly, 93, Time-varying and nonlinear models a) Smooth transition and threshold autoregressive models b) Neural networks c) Markov switching models d) ARCH and stochastic volatility models e) Example: comparison of several forecasting models for euro area and US macro variables (Forecasting with nonlinear models) f) Example: a multivariate TAR model for forecasting GDP growth (Time-varying VARs and international shock transmission) g) Example: a multivariate MS-ECM of the UK labour market (Impulse response functions in nonlinear models) h) Example: the great moderation in the US (SV and Bayesian time-varying models) Franses, P.H. and van Dijk, D. (2000), Nonlinear Time Series Models in Empirical Finance, Cambridge: Cambridge University Press. (Ch. 3, 5) Hamilton, J.D., (1994), Time Series Analysis, Princeton: Princeton University Press. (Ch. 21, 22) Harvey, A. (1993), Time Series Models, London: Harvester. (Ch 8) Artis, M. J., Galvao, A. B. and M. Marcellino (2007), "The transmission mechanism in a changing world", Journal of Applied Econometrics, 22, Cogley, T. and Sargent, T. (2005), "Drift and Volatilities: Monetary Policies and Outcomes in the Post WWII U.S," Review of Economic Dynamics, vol. 8(2), Krolzig, H-M, Marcellino, M. and Mizon, G.E. (2002) A Markov-switching vector equilibrium correction model of the UK labour market, Empirical Economics, 27, Marcellino, M. (2004a), Forecasting EMU macroeconomic variables, International Journal of Forecasting, 20, Sims, C and Zha T. (2006), "Were There Regime Switches in U.S. Monetary Policy?," American Economic Review, 96(1), Stock, J. H. and M. W. Watson (1999), " A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series", in: Cointegration, Causality, and Forecasting - Festschrift in Honour of Clive W. J. Granger, edited by R. Engle and H. White Stock, J. H. and Watson, M. W. (2007), Why has inflation become harder to forecast?, Journal of Money Credit and Banking, 39,

3 3. The Kalman Filter a) State space representation of dynamic linear models b) Structural time series models c) Derivation of the Kalman filter d) Forecasting e) Maximum likelihood estimation f) Example: the Stock-Watson coincident index for the US (Small scale factor model) g) Example: the Mariano-Murasawa coincident index for the US (Mixed frequency data) h) Example: the Kim-Yoo coincident index for the US (Markov switching factor model) i) Example: Ireland s sticky price model (MLE of a DSGE model) j) Example: MIDAS models vs mixed frequency VAR (alternative approaches for mixed data) Hamilton, J.D., (1994), Time Series Analysis, Princeton: Princeton University Press. (Ch. 13) Luetkepohl, H., (2005), New Introduction to Multiple Time Series Analysis, Springer (Ch. 18) Harvey, A. (1993), Time Series Models, London: Harvester. (Ch 4, 5) Kim, C-J. and Nelson C.R. (1999), State space models with regime switching, Cambridge: MIT Press (Ch. 3-5) Canova, F. (2007), Methods for Applied Macroeconomic Research, Princeton: Princeton University Press. (Ch. 6) Ireland, P.N., (2001), " Sticky-Price Models of the Business Cycle: Specification and Stability", Journal of Monetary Economics, 47, Kim, M.-J. and J.-S. Yoo (1995), "New index of coincident indicators: a multivariate Markov switching factor model approach", Journal of Monetary Economics, 36: Mariano, R. and Murasawa, J. (2003), "A new coincident index of business cycles based on monthly and quarterly series," Journal of Applied Econometrics, vol. 18(4), pages Stock, J. H. and Watson, M. W. (1989). New indexes of coincident and leading economic indicators, in: Blanchard, O., and S. Fischer, eds., NBER Macroeconomics Annual, MIT Press (Cambridge, MA), Kuzin, V., Marcellino, M and Schumacher, C. (2011) MIDAS vs Mixed-Frequency VAR for Nowcasting GDP in the Euro Area, International Journal of Forecasting, 27, Methods for the analysis of large datasets a) Factor models: representation and principal component based estimation b) Shrinkage estimators and Bayesian methods c) Reduced rank regressions d) Variable selection: information criteria, LASSO and Boosting e) Example: factor based forecasts of euro area, US and UK macro variables f) Example: factor based interpolation, backdating, and nowcasting g) Example: the role of factors in Taylor rules and monetary VARs for the euro area and the US h) Example: factor augmented error correction models i) Example: forecast comparison of alternative methods

4 j) Example: time-varying factor models Angelini, E., Henry, J. and Marcellino, M. (2006) Interpolation with a large information set, Journal of Economic Dynamics and Contro l, 30, Artis, M., Banerjee, A. and Marcellino, M. (2005), Factor Forecasts for the UK, Journal of Forecasting, 24, Bai, J. (2003), Inferential Theory for Factor Models of Large Dinensions," Econometrica, 71, Bai, J., and S. Ng (2006), "Confidence intervals for diffusion index forecasts with a large number of preditors", Econometrica, 74, Bai, J., and S. Ng (2007), Boosting diffusion indexes, mimeo. Banerjee, A. and Marcellino, M. (2009), Factor augmented error correction models, in Castle, J. and Shepard, N. (Eds.), The Methodology and Practice of Econometrics A Festschrift for David Hendry, Oxford: Oxford University Press, forthcoming Carriero, A., Kapetanios, G., Marcellino, M. (2010) Forecasting Large Datasets with Bayesian Reduced Rank Multivariate Models, Journal of Applied Econometrics, forthcoming De Mol, C., Giannone, D. and Reichlin, L. (2006), "Forecasting using a Large Number of Predictors: Is Bayesian Regression a Valid Alternative to Principal Components?" ECB Working Paper No Eickmeier, S., Lemke, W. and Marcellino, M. (2011) A Classical Time Varying FAVAR Model: Estimation, Forecasting, and Structural Analysis, CEPR WP Favero, C.A., Marcellino, M., Neglia, F. (2005) Principal components at work: the empirical analysis of monetary policy with large datasets, Journal of Applied Econometrics, 20, Forni, M., Hallin, M., Lippi, M. and Reichlin, L. (2000), The Generalized Dynamic Factor Model: Identification and Estimation Review of Economics and Statistics, 11, pp Kapetanios, G. and Marcellino, M. (2009), A Parametric Estimation Method for Dynamic Factor Models of Large Dimensions, Journal of Time Series Analysis, 30, Kapetanios, G. and Marcellino, M. (2010), Factor GMM estimation with a large set of possibly weak instruments, Computational Statistics and Data Analysis, 54, Marcellino, M., Stock, J.H. and Watson, M.W. (2003), Macroeconomic Forecasting in the Euro Area: Country Specific Versus Euro Wide Information, European Economic Review, 47, pp Stock, J. H. and M. W. Watson (2002a), Macroeconomic Forecasting Using Diffusion Indexes, Journal of Business and Economic Statistics, 20, Stock, J. H. and Watson, M. W. (2002b), Forecasting Using Principal Components from a Large Number of Predictors, Journal of the American Statistical Association, 97, Stock, J. H. and Watson, M. W. (2006), Forecasting with many predictors, in G. Elliott, C. Granger, A. Timmermann, (eds.), Handbook of Economic Forecasting, Elsevier-North Holland

5 Dates of lectures and classes: L1: Friday 20 April, L2: Monday 23 April, L3: Tuesday 24 April, TA1: Wednesday 25 April, L4: Wednesday 25 April, L5: Monday 30 April, TA2: Wednesday 2 May, L6: Thursday 3 May, 8.45 L7: Monday 7 May, TA3: Wednesday 9 May, L8: Friday 11 May, 8.45 TA4: Wednesday 16 May, L9: Thursday 17 May, 8.45 L10: Friday 18 May, 8.45 TA5: Wednesday 23 May, Problem sets - deadlines PS1: PS2: PS3: Wednesday 25 April due: Wednesday 9 May Wednesday 9 May due: Monday 21 May Wednesday 23 May due: Friday 1 June Exam Monday 28 May,

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