We extend the “bottom up” approach for forecasting economic aggregates with disaggregates to probability forecasting. Our methodology utilises a linear opinion pool to combine the forecast densities from many disaggregate forecasting specifications, using weights based on the continuous ranked probability score. We also adopt a post-processing step prior to forecast combination. These methods are adapted from the meteorology literature. In our application, we use our approach to forecast US Personal Consumption Expenditure inflation from 1990q1 to 2009q4. Our ensemble combining the evidence from 16 disaggregate PCE series outperforms an integrated moving average specification for aggregate inflation in terms of density forecasting.
Atger, F. 2003. “Spatial and Interannual Variability of the Reliability of Ensemble-based Probabilistic Forecasts: Consequences for Calibration.” Monthly Weather Review 131: 1509–1523.
Amisano, G., and R. Giacomini. 2007. “Comparing Density Forecasts via Likelihood Ratio Tests.” Journal of Business and Economic Statistics 25 (2): 177–190.
Arora, S. M., M. A. Little, and P. E. McSharry. 2013. “Nonlinear and Nonparametric Modelling Approaches for Forecasting the US GNP.” Studies in Nonlinear Dynamics and Control, 1–26, published online June 2013.
Bache, I. W., J. Mitchell, F. Ravazzolo, and S. P. Vahey. 2010. “Macro Modeling with Many Models.” In Twenty Years of Inflation Targeting: Lessons Learned and Future Prospects, edited by D. Cobham, Ø. Eitrheim, S. Gerlach, and J. Qvigstad, 398–418. Cambridge, UK: Cambridge University Press.
Bao, Y., T. -H. Lee, and B. Saltoglu. 2007. “Comparing Density Forecast Models.” Journal of Forecasting 26: 203–225.
Bao, L., T. Gneiting, E. P. Grimit, P. Guttop, and A. E. Raftery. 2010. “Bias Correction and Bayesian Model Averaging for Ensemble Forecasts of Surface Wind Direction.” Monthly Weather Review 138: 1811–1821.
Berkowitz, J. 2001. “Testing Density Forecasts, with Applications to Risk Management.” Journal of Business and Economic Statistics 19 (4): 465–474.
Clark, T. E. 2006. “Disaggregate Evidence on the Persistence of Consumer Price Inflation.” Journal of Applied Econometrics 21: 563–587.
Clark, T. E. 2011. “Real-time Density Forecasts from VARs with Stochastic Volatility.” Journal of Business and Economic Statistics 29 (3): 327–341.
Clark, T. E., and M. W. McCracken. 2010. “Averaging Forecasts from VARs with Uncertain Instabilities.” Journal of Applied Econometrics 25: 5–29.
Croushore, D. 2009. “Revisions to PCE Inflation Measures: Implications for Monetary Policy.” FRB Philadelphia Working Paper 08-8, revised July 2009.
Doblas-Reyes, F. J., A. Weisheimer, M. Déqué, N. Keenlyside, M. McVean, J. M. Murphy, P. Rogel, D. Smith, and T. N. Palmer. 2009. “Addressing Model Uncertainty in Seasonal and Annual Dynamical Ensemble Forecasts.” Quarterly Journal of the Royal Meteorological Society 135: 1538–1559.
Diebold, F. X., T. A. Gunther, and A. S. Tay. 1998. “Evaluating Density Forecasts; with Applications to Financial Risk Management.” International Economic Review 39: 863–883.
Feinstein, M., M. A. King, and J. Yellen. 2004. “Innovations and Issues in Monetary Policy: Panel Discussion.” American Economic Review, Papers and Proceedings, May, 41–48.
Garratt, A., J. Mitchell, S. P. Vahey, and Wakerly. 2011. “Real-time Inflation Forecast Densities from Ensemble Phillips Curves.” North American Journal of Economics and Finance 22: 77–87.
Geweke, J. 2009. Complete and Incomplete Econometric Models. Princeton, US: Princeton University Press.
Gneiting, T. 2011. “Making and Evaluating Point Forecasts.” Journal of the American Statistical Association 106: 746–762.
Gneiting, T., and A. E. Raftery. 2007. “Strictly Proper Scoring Rules, Prediction and Estimation.” Journal of the American Statistical Society 102 (477): 359–378.
Granger, C., and M. H. Pesaran. 2000. “Economic and Statistical Measures of Forecast Accuracy.” Journal of Forecasting 19: 537–560.
Greenspan, A. 2004. “Risk and Uncertainty in Monetary Policy.” American Economic Review, Papers and Proceedings, May, 33–40.
Groen, J. J. J., R. Paap, and F. Ravazzolo. 2009. “Real-time Inflation Forecasting in a Changing World.” Federal Reserve Bank of New York Staff Reports, 388.
Hendry, D. F., and K. Hubrich. 2011. “Combining Disaggregate Forecasts or Combining Disaggregate Information to Forecast an Aggregate.” Journal of Business and Economic Statistics 29 (2): 216–227.
Hersbach, H. 2000. “Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems.” Weather and Forecasting 15: 559–570.
Jore, A. S., J. Mitchell, and S. P. Vahey. 2010. “Combining Forecast Densities from VARs with Uncertain Instabilities.” Journal of Applied Econometrics 25: 621–634.
Kascha, C., and F. Ravazzolo. 2010. “Combining Inflation Density Forecasts.” Journal of Forecasting 29: 231–250.
Koop, G. 2003. Bayesian Econometrics, Chichester, UK: Wiley.
Lütkepohl, H. 2009. “Forecasting Aggregated Time Series Variables: A Survey.” Economics Working Papers ECO2009/17, European University Institute.
Lütkepohl, H. 2010. “Forecasting Nonlinear Aggregates and Aggregates with Time-varying Weights.” Economics Working Papers ECO2010/11, European University Institute.
Marcellino, M., J. Stock, and M. Watson. 2003. “Macroeconomic Forecasting in the Euro area: Country Specific versus Euro Wide Information.” European Economic Review 47: 1–18.
Mitchell, J., and S. G. Hall. 2005. “Evaluating, Comparing and Combining Density Forecasts using the KLIC with an Application to the Bank of England and NIESR Fan Charts of Inflation.” Oxford Bulletin of Economics and Statistics 67: 995–1033.
Mitchell, J., and K. F. Wallis. 2011. “Evaluating Density Forecasts: Forecast Combinations, Model Mixtures, Calibration and Sharpness.” Journal of Applied Econometrics 26: 1023–1040.
Panagiotelis, A., and M. Smith. 2008. “Bayesian Density Forecasting Intraday Electricity Prices using Multivariate Skew t Distribution.” International Journal of Forecasting 24: 710–727.
Raftery, A. E., T. Gneiting, F. Balabdaoui, and M. Polakowski. 2005. “Using Bayesian Model Averaging to Calibrate Forecast Ensembles.” Monthly Weather Review 133: 1155–1174.
Rosenblatt, M. 1952. “Remarks on a Multivariate Transformation.” The Annals of Mathematical Statistics 23: 470–472.
Stensrud, D. J., and N. Yussouf. 2007. “Bias-corrected Short-range Ensemble Forecasts of Near Surface Variables.” Meteorological Applications 12: 217–230.
Stock, J. H., and M. W. Watson. 2007. “Why has US Inflation Become Harder to Forecast?” Journal of Money, Credit and Banking 39: 3–34.
Timmermann, A. 2006. “Forecast Combinations.” in Handbook of Economic Forecasting, vol. 1, edited by G. Elliot, C. Granger, and A. Timmermann, 135–196. North-Holland.
van Garderen, K. J, K. Lee, and M. H. Pesaran. 2000. “Cross-sectional Aggregation of Non-linear Models.” Journal of Econometrics 95: 285–331.
Wallis, K. F. 2003. “Chi-squared Tests of Interval and Density Forecasts, and the Bank of England’s Fan Charts.” International Journal of Forecasting 19: 165–175.
Wallis, K. F. 2005. “Combining Density and Interval Forecasts: a Modest Proposal.” Oxford Bulletin of Economics and Statistics 67: 983–994.
SNDE recognizes that advances in statistics and dynamical systems theory can increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.