Forecast densities for economic aggregates from disaggregate ensembles

Abstract 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.

[1]  T. Gneiting.  Making and Evaluating Point Forecasts , 2009, 0912.0902.

[2]  A. Timmermann,et al.  Forecasts of Us Short-Term Interest Rates: A Flexible Forecast Combination Approach , 2006 .

[3]  J. Stock,et al.  Why Has U.S. Inflation Become Harder to Forecast , 2007 .

[4]  Shaun P. Vahey,et al.  Measuring Core Inflation in Australia with Disaggregate Ensembles , 2010 .

[5]  H. Lütkepohl.  Forecasting Nonlinear Aggregates and Aggregates with Time-varying Weights , 2010, SSRN Electronic Journal.

[6]  R. I. Phelps.  Forecast Combination , 1981 .

[7]  C. N. Morris,et al.  The calculation of posterior distributions by data augmentation , 1987 .

[8]  A. Raftery,et al.  Using Bayesian Model Averaging to Calibrate Forecast Ensembles , 2005 .

[9]  Max A. Little,et al.  Nonlinear and nonparametric modeling approaches for probabilistic forecasting of the US gross national product , 2013 .

[10]  John Geweke,et al.  Complete and Incomplete Econometric Models , 2010 .

[11]  Jeremy Berkowitz.  Testing Density Forecasts, With Applications to Risk Management , 2001 .

[12]  Time-varying Weights.  Forecasting Nonlinear Aggregates and Aggregates with , 2011 .

[13]  Kenneth F. Wallis,et al.  Combining Density and Interval Forecasts: A Modest Proposal , 2005 .

[14]  C. Granger,et al.  Economic and Statistical Measures of Forecast Accuracy , 1999 .

[15]  Francesco Ravazzolo,et al.  Real-Time Inflation Forecasting in a Changing World , 2009 .

[16]  D. Hendry,et al.  Combining Disaggregate Forecasts or Combining Disaggregate Information to Forecast an Aggregate , 2009, SSRN Electronic Journal.

[17]  Simon M. Potter,et al.  Estimation and forecasting in models with multiple breaks , 2007 .

[18]  H. Hersbach.  Decomposition of the Continuous Ranked Probability Score for Ensemble Prediction Systems , 2000 .

[19]  Kenneth F. Wallis,et al.  Chi-Squared Tests of Interval and Density Forecasts, and the Bank of England's Fan Charts , 2001, SSRN Electronic Journal.

[20]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  N. Shephard.  Partial non-Gaussian state space , 1994 .

[22]  Helmut Lütkepohl,et al.  Forecasting Aggregated Time Series Variables: A Survey , 2011 .

[23]  Sveriges Riksbank.  Efficient Bayesian inference for multiple change-point and mixture innovation models , 2006 .

[24]  M. Rosenblatt.  Remarks on a Multivariate Transformation , 1952 .

[25]  Anthony S. Tay,et al.  Evaluating Density Forecasts with Applications to Financial Risk Management , 1998 .

[26]  Robert Kohn,et al.  Semiparametric Bayesian Inference for Time Series with Mixed Spectra , 1996 .

[27]  Shaun P. Vahey,et al.  Real-Time Inflation Forecast Densities from Ensemble Phillips Curves , 2010 .

[28]  Tilmann Gneiting,et al.  Predicting Inflation: Professional Experts Versus No-Change Forecasts , 2010 .

[29]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[30]  M. Hashem Pesaran,et al.  Cross-sectional aggregation of non-linear models , 2000 .

[31]  Norman R. Swanson,et al.  Predictive Density Evaluation , 2005 .

[32]  Todd E. Clark.  Real-Time Density Forecasts from VARs with Stochastic Volatility , 2009 .

[33]  Anastasios Panagiotelis,et al.  Bayesian Density Forecasting of Intraday Electricity Prices using Multivariate Skew t Distributions , 2008 .

[34]  Robert L. Wilby,et al.  From climate model ensembles to climate change impacts and adaptation: A case study of water resource management in the southwest of England , 2009 .

[35]  GuptaSunil,et al.  Combination of Forecasts , 1987 .

[36]  Anthony S. Tay,et al.  Evaluating Density Forecasts , 1997 .

[37]  Gianni Amisano,et al.  Comparing Density Forecasts via Weighted Likelihood Ratio Tests , 2007 .

[38]  Alan Greenspan,et al.  Risk and Uncertainty in Monetary Policy , 2004 .

[39]  R. Kohn,et al.  On Gibbs sampling for state space models , 1994 .

[40]  Todd E. Clark.  Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility , 2011 .

[41]  Francesco Ravazzolo,et al.  Combining inflation density forecasts , 2010 .

[42]  R. Kohn,et al.  Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models , 2005 .

[43]  Francesco Ravazzolo,et al.  The Power of Weather , 2009, Comput. Stat. Data Anal..

[44]  Yong Bao,et al.  Comparing Density Forecast Models , 2007 .

[45]  Shaun P. Vahey,et al.  Combining forecast densities from VARs with uncertain instabilities , 2010 .

[46]  J. M. Bates,et al.  The Combination of Forecasts , 1969 .

[47]  James Mitchell,et al.  Evaluating, Comparing and Combining Density Forecasts Using the Klic with an Application to the Bank of England and Niesr 'Fan' Charts of Inflation , 2005 .

[48]  F. Atger,et al.  Spatial and Interannual Variability of the Reliability of Ensemble-Based Probabilistic Forecasts: Consequences for Calibration , 2003 .

[49]  F. Molteni,et al.  The ECMWF Ensemble Prediction System: Methodology and validation , 1996 .

[50]  J. Stock,et al.  Forecasting Output and Inflation: The Role of Asset Prices , 2001 .

[51]  T. Palmer,et al.  Addressing model uncertainty in seasonal and annual dynamical ensemble forecasts , 2009 .

[52]  J. Stock,et al.  Macroeconomic forecasting in the Euro area: Country specific versus area-wide information , 2003 .

[53]  Todd E. Clark,et al.  Averaging Forecasts from Vars with Uncertain Instabilities , 2006 .

[54]  Adrian E. Raftery,et al.  Bias Correction and Bayesian Model Averaging for Ensemble Forecasts of Surface Wind Direction , 2010 .

[55]  R. Kohn,et al.  Efficient Bayesian Inference for Dynamic Mixture Models , 2000 .

[56]  James Mitchell,et al.  Measuring Output Gap Uncertainty , 2009 .

[57]  Todd E. Clark.  Disaggregate Evidence on the Persistence of Consumer Price Inflation , 2003 .

[58]  A. Harvey,et al.  5 Stochastic volatility , 1996 .

[59]  Janet L. Yellen,et al.  Innovations and Issues in Monetary Policy: Panel Discussion , 2004 .

[60]  N. Shephard,et al.  Stochastic Volatility: Likelihood Inference And Comparison With Arch Models , 1996 .

[61]  David J. Stensrud,et al.  Bias‐corrected short‐range ensemble forecasts of near surface variables , 2005 .

[62]  James Mitchell,et al.  Evaluating density forecasts: forecast combinations, model mixtures, calibration and sharpness , 2011 .

[63]  D. Croushore,et al.  Revisions to PCE Inflation Measures: Implications for Monetary Policy , 2008 .