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Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors

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  • Todd E. Clark

    (Federal Reserve Bank of Cleveland)

  • Michael W. McCracken

    (Federal Reserve Bank of St. Louis)

  • Elmar Mertens

    (Deutsche Bundesbank)

Abstract

We estimate uncertainty measures for point forecasts obtained from survey data, pooling information embedded in observed forecast errors for different forecast horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon specification of stochastic volatility. We apply our method to forecasts for various macroeconomic variables from the Survey of Professional Forecasters. Compared to simple variance approaches, our stochastic volatility model improves the accuracy of uncertainty measures for survey forecasts.

Suggested Citation

  • Todd E. Clark & Michael W. McCracken & Elmar Mertens, 2020. "Modeling Time-Varying Uncertainty of Multiple-Horizon Forecast Errors," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 17-33, March.
  • Handle: RePEc:tpr:restat:v:102:y:2020:i:1:p:17-33
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    1. Knüppel, Malte, 2014. "Efficient estimation of forecast uncertainty based on recent forecast errors," International Journal of Forecasting, Elsevier, vol. 30(2), pages 257-267.
    2. Diebold, Francis X. & Schorfheide, Frank & Shin, Minchul, 2017. "Real-time forecast evaluation of DSGE models with stochastic volatility," Journal of Econometrics, Elsevier, vol. 201(2), pages 322-332.
    3. Chiu, Ching-Wai (Jeremy) & Mumtaz, Haroon & Pintér, Gábor, 2017. "Forecasting with VAR models: Fat tails and stochastic volatility," International Journal of Forecasting, Elsevier, vol. 33(4), pages 1124-1143.
    4. Croushore, Dean & Stark, Tom, 2001. "A real-time data set for macroeconomists," Journal of Econometrics, Elsevier, vol. 105(1), pages 111-130, November.
    5. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    6. Christopher A. Sims, 2002. "The Role of Models and Probabilities in the Monetary Policy Process," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 33(2), pages 1-62.
    7. Andrea Carriero & Todd E. Clark & Massimiliano Marcellino, 2016. "Common Drifting Volatility in Large Bayesian VARs," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 375-390, July.
    8. Clements, Michael P., 2018. "Are macroeconomic density forecasts informative?," International Journal of Forecasting, Elsevier, vol. 34(2), pages 181-198.
    9. James H. Stock & Mark W. Watson, 2016. "Core Inflation and Trend Inflation," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 770-784, October.
    10. Cogley, Timothy & Morozov, Sergei & Sargent, Thomas J., 2005. "Bayesian fan charts for U.K. inflation: Forecasting and sources of uncertainty in an evolving monetary system," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1893-1925, November.
    11. Andrew Patton & Allan Timmermann, 2012. "Forecast Rationality Tests Based on Multi-Horizon Bounds," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 1-17.
    12. Soojin Jo & Rodrigo Sekkel, 2019. "Macroeconomic Uncertainty Through the Lens of Professional Forecasters," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 436-446, July.
    13. Alejandro Justiniano & Giorgio E. Primiceri, 2008. "The Time-Varying Volatility of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 98(3), pages 604-641, June.
    14. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    15. Rossi, Barbara & Sekhposyan, Tatevik, 2014. "Evaluating predictive densities of US output growth and inflation in a large macroeconomic data set," International Journal of Forecasting, Elsevier, vol. 30(3), pages 662-682.
    16. Vasco Cúrdia & Marco Del Negro & Daniel L. Greenwald, 2014. "Rare Shocks, Great Recessions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(7), pages 1031-1052, November.
    17. Michael P. Clements, 2014. "Forecast Uncertainty- Ex Ante and Ex Post : U.S. Inflation and Output Growth," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 206-216, April.
    18. Geoff Kenny & Thomas Kostka & Federico Masera, 2014. "How Informative are the Subjective Density Forecasts of Macroeconomists?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(3), pages 163-185, April.
    19. Christopher A. Sims, 2007. "Monetary Policy Models," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 38(2), pages 75-90.
    20. James H. Stock & Mark W. Watson, 2007. "Erratum to "Why Has U.S. Inflation Become Harder to Forecast?"," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    21. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    22. Antonello D'Agostino & Luca Gambetti & Domenico Giannone, 2013. "Macroeconomic forecasting and structural change," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(1), pages 82-101, January.
    23. Olivier Coibion & Yuriy Gorodnichenko, 2015. "Information Rigidity and the Expectations Formation Process: A Simple Framework and New Facts," American Economic Review, American Economic Association, vol. 105(8), pages 2644-2678, August.
    24. Croushore Dean, 2010. "An Evaluation of Inflation Forecasts from Surveys Using Real-Time Data," The B.E. Journal of Macroeconomics, De Gruyter, vol. 10(1), pages 1-32, May.
    25. James H. Stock & Mark W. Watson, 2007. "Erratum to “Why Has U.S. Inflation Become Harder to Forecast?”," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    26. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    27. Giordani, Paolo & Villani, Mattias, 2010. "Forecasting macroeconomic time series with locally adaptive signal extraction," International Journal of Forecasting, Elsevier, vol. 26(2), pages 312-325, April.
    28. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    29. David H. Romer & Christina D. Romer, 2000. "Federal Reserve Information and the Behavior of Interest Rates," American Economic Review, American Economic Association, vol. 90(3), pages 429-457, June.
    30. Joshua Abel & Robert Rich & Joseph Song & Joseph Tracy, 2016. "The Measurement and Behavior of Uncertainty: Evidence from the ECB Survey of Professional Forecasters," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(3), pages 533-550, April.
    31. Todd E. Clark, 2011. "Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 327-341, July.
    32. Tilmann Gneiting & Roopesh Ranjan, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 411-422, July.
    33. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    34. Todd E. Clark & Francesco Ravazzolo, 2015. "Macroeconomic Forecasting Performance under Alternative Specifications of Time‐Varying Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(4), pages 551-575, June.
    35. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
    36. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    37. Malte Knüppel & Guido Schultefrankenfeld, 2012. "How Informative Are Central Bank Assessments of Macroeconomic Risks?," International Journal of Central Banking, International Journal of Central Banking, vol. 8(3), pages 87-139, September.
    38. Christopher A. Sims, 2007. "Monetary Policy Models," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 38(2), pages 75-90.
    39. Kajal Lahiri & Xuguang Sheng, 2010. "Measuring forecast uncertainty by disagreement: The missing link," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 514-538.
    40. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
    41. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    42. Kenneth F. Wallis, 2005. "Combining Density and Interval Forecasts: A Modest Proposal," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 983-994, December.
    43. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    44. Gneiting, Tilmann & Ranjan, Roopesh, 2011. "Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 411-422.
    45. repec:pri:cepsud:155sims is not listed on IDEAS
    46. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
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    2. Li, Zheng & Zeng, Jingjing & Hensher, David A., 2023. "An efficient approach to structural breaks and the case of automobile gasoline consumption in Australia," Transportation Research Part A: Policy and Practice, Elsevier, vol. 169(C).
    3. Li, Zheng & Zhou, Bo & Hensher, David A., 2022. "Forecasting automobile gasoline demand in Australia using machine learning-based regression," Energy, Elsevier, vol. 239(PD).
    4. Oliver Grothe & Fabian Kachele & Fabian Kruger, 2022. "From point forecasts to multivariate probabilistic forecasts: The Schaake shuffle for day-ahead electricity price forecasting," Papers 2204.10154, arXiv.org.
    5. Efrem Castelnuovo, 2022. "Uncertainty Before and During COVID-19: A Survey," "Marco Fanno" Working Papers 0279, Dipartimento di Scienze Economiche "Marco Fanno".
    6. Knüppel, Malte & Schultefrankenfeld, Guido, 2019. "Assessing the uncertainty in central banks’ inflation outlooks," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1748-1769.
    7. Ana Beatriz Galvão & James Mitchell, 2023. "Real‐Time Perceptions of Historical GDP Data Uncertainty," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 457-481, June.
    8. Adams, Patrick A. & Adrian, Tobias & Boyarchenko, Nina & Giannone, Domenico, 2021. "Forecasting macroeconomic risks," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1173-1191.
    9. Galvão, Ana Beatriz & Garratt, Anthony & Mitchell, James, 2021. "Does judgment improve macroeconomic density forecasts?," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1247-1260.
    10. Corradi, Valentina & Fosten, Jack & Gutknecht, Daniel, 2023. "Out-of-sample tests for conditional quantile coverage an application to Growth-at-Risk," Journal of Econometrics, Elsevier, vol. 236(2).
    11. Reifschneider, David & Tulip, Peter, 2019. "Gauging the uncertainty of the economic outlook using historical forecasting errors: The Federal Reserve’s approach," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1564-1582.
    12. Grothe, Oliver & Kächele, Fabian & Krüger, Fabian, 2023. "From point forecasts to multivariate probabilistic forecasts: The Schaake shuffle for day-ahead electricity price forecasting," Energy Economics, Elsevier, vol. 120(C).
    13. Simón Sosvilla-Rivero & María del Carmen Ramos-Herrera, 2018. "Inflation, real economic growth and unemployment expectations: an empirical analysis based on the ECB survey of professional forecasters," Applied Economics, Taylor & Francis Journals, vol. 50(42), pages 4540-4555, September.
    14. Marcellino, Massimiliano & Clark, Todd & Carriero, Andrea & Mertens, Elmar, 2021. "Addressing COVID-19 Outliers in BVARs with Stochastic Volatility," CEPR Discussion Papers 15964, C.E.P.R. Discussion Papers.
    15. Knüppel, Malte, 2018. "Forecast-error-based estimation of forecast uncertainty when the horizon is increased," International Journal of Forecasting, Elsevier, vol. 34(1), pages 105-116.
    16. Dibiasi, Andreas & Sarferaz, Samad, 2023. "Measuring macroeconomic uncertainty: A cross-country analysis," European Economic Review, Elsevier, vol. 153(C).
    17. Barbara Rossi, 2018. "Identifying and estimating the effects of unconventional monetary policy in the data: How to do It and what have we learned?," Economics Working Papers 1641, Department of Economics and Business, Universitat Pompeu Fabra, revised Jul 2020.
    18. Tamás Kiss & Stepan Mazur & Hoang Nguyen & Pär Österholm, 2023. "Modeling the relation between the US real economy and the corporate bond‐yield spread in Bayesian VARs with non‐Gaussian innovations," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(2), pages 347-368, March.
    19. Fabian Kruger & Hendrik Plett, 2022. "Prediction intervals for economic fixed-event forecasts," Papers 2210.13562, arXiv.org, revised Mar 2024.
    20. Mirela Miescu, 2019. "Uncertainty shocks in emerging economies," Working Papers 277077821, Lancaster University Management School, Economics Department.
    21. Barbara Rossi, 2019. "Forecasting in the Presence of Instabilities: How Do We Know Whether Models Predict Well and How to Improve Them," Working Papers 1162, Barcelona School of Economics.
    22. Bas Scheer, 2022. "Addressing Unemployment Rate Forecast Errors in Relation to the Business Cycle," CPB Discussion Paper 434, CPB Netherlands Bureau for Economic Policy Analysis.
    23. Weiqi Zhang & Huong Ha & Hui Ting Evelyn Gay, 2020. "Analysts’ forecasts between last consensus and earning announcement date," Journal of Financial Reporting and Accounting, Emerald Group Publishing Limited, vol. 18(4), pages 779-793, November.
    24. Todd E. Clark & Gergely Ganics & Elmar Mertens, 2022. "What is the Predictive Value of SPF Point and Density Forecasts?," Working Papers 22-37, Federal Reserve Bank of Cleveland.
    25. Sharpe, Steven A. & Sinha, Nitish R. & Hollrah, Christopher A., 2023. "The power of narrative sentiment in economic forecasts," International Journal of Forecasting, Elsevier, vol. 39(3), pages 1097-1121.

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    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

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