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ARCH models for multi-period forecast uncertainty-a reality check using a panel of density forecasts

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  • Lahiri, Kajal
  • Liu, Fushang

Abstract

We develop a theoretical framework to compare forecast uncertainty estimated from time series models to those available from survey density forecasts. The sum of the average variance of individual densities and the disagreement, which is the same as the variance of the aggregate density, is shown to approximate the predictive uncertainty from well specified time series models when the variance of the aggregate shocks is relatively small compared to that of the idiosyncratic shocks. We argue that due to grouping error problems, compositional effects of the panel, and other complications, the uncertainty measure has to be estimated from individual densities. Despite numerous reservations on the credibility of time series based measures of forecast uncertainty, we found that during normal times the uncertainty estimates based on ARCH models simulate the subjective survey measure remarkably well. However, during times of regime change and structural break, the two estimates do not overlap. We suggest ways to improve the time series measures during periods when forecast errors are apt to be large. The disagreement series is a good indicator of such periods.

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  • Lahiri, Kajal & Liu, Fushang, 2005. "ARCH models for multi-period forecast uncertainty-a reality check using a panel of density forecasts," MPRA Paper 21693, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:21693
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    1. Palm, F. & Zellner, A., 1991. "To combine or not to combine? issues of combining forecasts," LIDAM Discussion Papers CORE 1991022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Mordecai Kurz & Maurizio Motolese, "undated". "Endogenous Uncertainty and Market Volatility," Working Papers 99005, Stanford University, Department of Economics.
    3. N. Gregory Mankiw & Ricardo Reis, 2002. "Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1295-1328.
    4. Lahiri, Kajal & Teigland, Christie & Zaporowski, Mark, 1988. "Interest Rates and the Subjective Probability Distribution of Inflation Forecasts," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 20(2), pages 233-248, May.
    5. N. Gregory Mankiw & Ricardo Reis & Justin Wolfers, 2004. "Disagreement about Inflation Expectations," NBER Chapters, in: NBER Macroeconomics Annual 2003, Volume 18, pages 209-270, National Bureau of Economic Research, Inc.
    6. Kajal Lahiri, 2005. "Analysis of Panel Data," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(4), pages 1093-1095.
    7. Robert W. Rich & Joseph Tracy, 2003. "Modeling uncertainty: predictive accuracy as a proxy for predictive confidence," Staff Reports 161, Federal Reserve Bank of New York.
    8. Christoffersen, Peter F. & Diebold, Francis X., 1997. "Optimal Prediction Under Asymmetric Loss," Econometric Theory, Cambridge University Press, vol. 13(6), pages 808-817, December.
    9. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
    10. Francis X. Diebold & Anthony S. Tay & Kenneth F. Wallis, 1997. "Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters," NBER Working Papers 6228, National Bureau of Economic Research, Inc.
    11. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
    12. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    13. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    14. Bomberger, William A, 1996. "Disagreement as a Measure of Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(3), pages 381-392, August.
    15. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    16. Victor Zarnowitz & Louis A. Lambros, 1983. "Consensus and Uncertainty in Economic Prediction," NBER Working Papers 1171, National Bureau of Economic Research, Inc.
    17. Levi, Maurice D & Makin, John H, 1978. "Anticipated Inflation and Interest Rates: Further Interpretation of Findings on the Fisher Equation," American Economic Review, American Economic Association, vol. 68(5), pages 801-812, December.
    18. Lucas, Robert E, Jr, 1973. "Some International Evidence on Output-Inflation Tradeoffs," American Economic Review, American Economic Association, vol. 63(3), pages 326-334, June.
    19. Christopher D. Carroll, 2003. "Macroeconomic Expectations of Households and Professional Forecasters," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(1), pages 269-298.
    20. Giordani, Paolo & Soderlind, Paul, 2003. "Inflation forecast uncertainty," European Economic Review, Elsevier, vol. 47(6), pages 1037-1059, December.
    21. Laurence Ball & N. Gregory Mankiw, 1995. "Relative-Price Changes as Aggregate Supply Shocks," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 161-193.
    22. Kastens, Terry L. & Schroeder, Ted C. & Plain, Ronald L., 1998. "Evaluation Of Extension And Usda Price And Production Forecasts," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 23(1), pages 1-18, July.
    23. Garratt A. & Lee K. & Pesaran M.H. & Shin Y., 2003. "Forecast Uncertainties in Macroeconomic Modeling: An Application to the U.K. Economy," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 829-838, January.
    24. Roy Batchelor & Pami Dua, 1995. "Forecaster Diversity and the Benefits of Combining Forecasts," Management Science, INFORMS, vol. 41(1), pages 68-75, January.
    25. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    26. Lahiri, Kajal & Teigland, Christie, 1987. "On the normality of probability distributions of inflation and GNP forecasts," International Journal of Forecasting, Elsevier, vol. 3(2), pages 269-279.
    27. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    28. Croushore, Dean & Stark, Tom, 2001. "A real-time data set for macroeconomists," Journal of Econometrics, Elsevier, vol. 105(1), pages 111-130, November.
    29. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    30. Cukierman, Alex & Wachtel, Paul, 1982. "Relative Price Variability and Nonuniform Inflationary Expectations," Journal of Political Economy, University of Chicago Press, vol. 90(1), pages 146-157, February.
    31. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    32. Cukierman, Alex & Wachtel, Paul, 1979. "Differential Inflationary Expectations and the Variability of the Rate of Inflation: Theory and Evidence," American Economic Review, American Economic Association, vol. 69(4), pages 595-609, September.
    33. Evans, Martin & Wachtel, Paul, 1993. "Inflation Regimes and the," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 25(3), pages 475-511, August.
    34. 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.
    35. 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.
    36. Hsiao,Cheng & Pesaran,M. Hashem & Lahiri,Kajal & Lee,Lung Fei (ed.), 1999. "Analysis of Panels and Limited Dependent Variable Models," Cambridge Books, Cambridge University Press, number 9780521631693, November.
    37. Evans, Martin, 1991. "Discovering the Link between Inflation Rates and Inflation Uncertainty," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 23(2), pages 169-184, May.
    38. Charles F. Manski, 2004. "Measuring Expectations," Econometrica, Econometric Society, vol. 72(5), pages 1329-1376, September.
    39. Ball, Laurence, 1992. "Why does high inflation raise inflation uncertainty?," Journal of Monetary Economics, Elsevier, vol. 29(3), pages 371-388, June.
    40. Davies, Anthony & Lahiri, Kajal, 1995. "A new framework for analyzing survey forecasts using three-dimensional panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 205-227, July.
    41. David Laster & Paul Bennett & In Sun Geoum, 1999. "Rational Bias in Macroeconomic Forecasts," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(1), pages 293-318.
    42. Friedman, Milton, 1977. "Nobel Lecture: Inflation and Unemployment," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 451-472, June.
    43. Hlouskova, Jaroslava & Schmidheiny, Kurt & Wagner, Martin, 2009. "Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 330-336, March.
    44. Martin Evans & Paul Wachtel, 1993. "Inflation regimes and the sources of inflation uncertainty," Proceedings, Federal Reserve Bank of Cleveland, pages 475-520.
    45. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
    46. Fuhrer, Jeffrey C, 1988. "On the Information Content of Consumer Survey Expectations," The Review of Economics and Statistics, MIT Press, vol. 70(1), pages 140-144, February.
    47. Blair, Bevan J. & Poon, Ser-Huang & Taylor, Stephen J., 2001. "Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 5-26, November.
    48. 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.
    49. Zarnowitz, Victor & Lambros, Louis A, 1987. "Consensus and Uncertainty in Economic Prediction," Journal of Political Economy, University of Chicago Press, vol. 95(3), pages 591-621, June.
    50. Makin, John H, 1983. "Real Interest, Money Surprises, Anticipated Inflation and Fiscal Deficits," The Review of Economics and Statistics, MIT Press, vol. 65(3), pages 374-384, August.
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    Cited by:

    1. Atalla, Tarek & Joutz, Fred & Pierru, Axel, 2016. "Does disagreement among oil price forecasters reflect volatility? Evidence from the ECB surveys," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1178-1192.
    2. 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.
    3. Fushang Liu & Kajal Lahiri, 2006. "Modelling multi-period inflation uncertainty using a panel of density forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1199-1219.
    4. Hartmann, Matthias & Herwartz, Helmut & Ulm, Maren, 2017. "A comparative assessment of alternative ex ante measures of inflation uncertainty," International Journal of Forecasting, Elsevier, vol. 33(1), pages 76-89.
    5. Glas, Alexander & Hartmann, Matthias, 2016. "Inflation uncertainty, disagreement and monetary policy: Evidence from the ECB Survey of Professional Forecasters," Journal of Empirical Finance, Elsevier, vol. 39(PB), pages 215-228.
    6. Christian Grimme & Steffen Henzel & Elisabeth Wieland, 2014. "Inflation uncertainty revisited: a proposal for robust measurement," Empirical Economics, Springer, vol. 47(4), pages 1497-1523, December.

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    More about this item

    Keywords

    Inflation; Survey of Professional Forecasters; GARCH; Real time data.;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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