Lahiri, Kajal and Liu, Fushang (2005): ARCH models for multi-period forecast uncertainty-a reality check using a panel of density forecasts. Published in: Advances in Econometrics , Vol. 20, (2005): pp. 321-363.
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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.
|Item Type:||MPRA Paper|
|Original Title:||ARCH models for multi-period forecast uncertainty-a reality check using a panel of density forecasts|
|Keywords:||Inflation, Survey of Professional Forecasters, GARCH, Real time data.|
|Subjects:||C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C53 - Forecasting and Prediction Methods; Simulation Methods
E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E31 - Price Level; Inflation; Deflation
C - Mathematical and Quantitative Methods > C2 - Single Equation Models; Single Variables > C23 - Models with Panel Data; Longitudinal Data; Spatial Time Series
E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E37 - Forecasting and Simulation: Models and Applications
|Depositing User:||Kajal Lahiri|
|Date Deposited:||31. Mar 2010 05:32|
|Last Modified:||11. Feb 2013 20:43|
Baillie, R.T. and T. Bollerslev (1992), “Prediction in dynamic models with time-dependent conditional variance”, Journal of Econometrics, 52, 91-113.
Ball, L. (1992), “Why does high inflation raise inflation uncertainty?” Journal of Monetary Economics, 371-388.
Ball, L. and N.G. Mankiw (1995), “Relative-price changes as aggregate supply shocks”, Quarterly Journal of Economics, 110, 161-193.
Batchelor, R. and P. Dua (1993), “Survey vs. ARCH measures of uncertainty”, Oxford Bulletin of Economics and Statistics, 55, 341-353.
Batchelor, R. and P. Dua (1995), “Forecaster diversity and the benefits of combining forecasts”, Management Science, 41, 68-75.
Batchelor, R. and P. Dua (1996), “Empirical measures of inflation uncertainty: a cautionary note”, Applied Economics, 28, 333-341.
Bera, A.K. and Higgins, M.L. (1993), “ARCH models: properties, estimation and testing”, Journal of Economic Surveys, 7, 305-362.
Blair B.J., S.H. Poon and S.J. Taylor (2001), “Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index return”, Journal of econometrics, 105, 5-26.
Bollerslev, T. (1986), “Generalized autoregressive conditional heteroscedasticity”, Journal of Econometrics, 31, 307-327.
Bollerslev, T. (1990), “Modeling the coherence in short-run nominal exchange rates: A multivariate generalized ARCH model”, Review of Economics and Statistics, 72, 498-505.
Bollerslev, T., Chou, R.Y. and K.P. Kroner (1992), “ARCH modeling in finance: a review of theory and empirical evidence”, Journal of Econometrics, 52, 5-59.
Bomberger, W.A. (1996), “Disagreement as a measure of uncertainty”, Journal of Money, Credit and Banking, 28, 381-392.
Carroll, C.D. (2003), “Macroeconomic expectations of households and professional forecasters”, Quarterly Journal of Economics, 118, 269-298.
Christofferson, P.F., and F.X. Diebold (1997), “Optimal prediction under asymmetric loss”, Econometric Theory, 13, 808-817.
Cogley, T., S. Morozov and T. J. Sargent (2003), “Bayesian Fan Charts for U.K. Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System”, Draft, July 2003.
Croushore, D. and T. Stark (2001), “A real-time data set for macroeconomists”, Journal of econometrics, 105, 111-130. Cukierman, A. and P. Wachtel (1979), “Differential inflationary expectations and the variability of the rate of inflation: theory and evidence ”, American Economic Review, 69, 595-609.
Cukierman, A. and P. Wachtel (1982), “relative price variability and nonuniform inflationary expectations ”, Journal of Political Economy, 90, 146-157.
Davies, A. and K. Lahiri (1995), “A new framework for analyzing survey forecasts using three-dimensional panel data”, Journal of Econometrics, 68, 205-227.
Davies, A. and K. Lahiri (1999), “Re-examining the rational expectations hypothesis using panel data on multi-period forecasts” In Hsiao, C., Lahiri, K., Lee, L.F. and Pesaran, H. (Eds.) Analysis of Panels and Limited Dependent Variable Models. Cambridge: Cambridge University Press.
Diebold, F., A. Tay and K. Wallis (1999), “Evaluating Density Forecasts of Inflation: The Survey of Professional Forecasters,” in R. Engle and H. White (eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honor of Clive W.J. Granger, 76-90, 1999. Oxford: Oxford University Press.
Engle, R. (1982), “Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation”, Econometrica, 50, 987-1008.
Engle, R. (1983), “Estimates of the variance of U.S. inflation based upon the ARCH model”, Journal of Money, Credit and Banking, 15, 286-301.
Engle, R.F. and D. Kraft (1983), “Multiperiod forecast error variances of inflation estimated from ARCH models”, in: A. Zellner, ed., Applied time series analysis of economic data (Bureau of the Census, Washington, DC), 293-302.
Engle, R. F. and Watson, M.W. (1985), “The Kalman filter: applications to forecasting and rational-expectations models” in: Truman Bewley, ed., Advances in econometrics, Vol. I, Fifth World Congress of the Econometric Society.
Ericsson, N.R. (2003), “Forecast uncertainty in economic modeling” In understanding economic forecasts, edited by David F. Hendry and Neil R. Ericsson, 68-92, Cambridge and London, MIT Press.
Evans, M. (1991), “Discovering the link between inflation rates and inflation uncertainty”, Journal of Money, Credit and Banking, 23, 169-184.
Evans, M. and P. Wachtel (1993), “Inflation regimes and the sources of inflation uncertainty”, Journal of Money, Credit and Banking, 25, 475-511.
Friedman, M. (1977), “Nobel Lecture: inflation and unemployment”, The Journal of Political Economy, 85, 451-472.
Fuhrer, J.C., (1988), “On the information content of consumer survey expectations”, Review of Economics and Statistics, 70, No. 1, 140-144.
Fukford, S.L. (2002), “The Impact of monetary policy on the cross-sectional variance of expectations of inflation”, Stanford University, mimeo.
Garratt, A., K. Lee, M. H. Pesaran and Y. Shin (2003), “Forecast uncertainty in macroeconomic modelling: an application to the U.K. ecomomy”, Journal of the American Statistical Association, 98, 829-838.
Giordani, P. and P. Söderlind (2003), “Inflation forecast uncertainty”, European Economic Review, 47, 1037-1059.
Glosten, L., R. Jagannathan, and D. Runkle (1993), “On the relation between the expected value and the volatility of the nominal excess return on stocks”, Journal of Finance, 48, 1779-1801.
Greene, W.H., Econometric Analysis, 4th Edition, Prentice Hall, Upper Saddle River, New Jersey, 2000.
Harvey A., E. Ruiz and E. Sentana (1992), “Unobserved component time series models with ARCH disturbances”, Journal of Econometrics 52, 129-157.
Hlouskova J., K. Schmidheiny and M. Wagner (2004), “Multistep predictions for multivariate GARCH models: closed form solution and the value for portfolio management”, Draft, 2004.
Irwin, S.H., M.E. Gerlow and T.R. Liu (1994), “The forecasting performance of livestock futures prices: a comparison of USDA expert predictions”, Journal of Futures Markets, 14, 861-875.
Kastens, T. L., T.C. Schroeder and R. Plain (1998), “Evaluation of extension and USDA price and production forecasts”, Journal of Agricultural and Resource Economics, 23, 244-261.
Kim, C.-J. and C.R. Nelson (1998), State-Space Model with Regime-Switching: Classical and Gibbs-sampling Approaches with Applications, MIT Press: Cambridge, MA.
Kurz, M. (2002), “Heterogeneous forecasting and Federal Reserve information”, Stanford University, 2002, mimeo.
Kurz, M. and M. Motolese (2001), “Endogenous uncertainty and market volatility”, Economic Theory, 17, 497-544.
Lahiri, K., and D. Ivanova (1998), "A time series and cross sectional analysis of consumer sentiment and its components", In Social Structural Change - Consequences for Business Cycle Surveys, (Eds. K. H. Oppenländer and G. Poser), Aldershot: Ashgate Publishing, England, 337-362.
Lahiri, K. and C. Teigland (1987), “On the normality of probability distribution and GNP forecasts”, International Journal of Forecasting, 3, 269-279.
Lahiri, K., C. Teigland and M. Zaporowski (1988), “Interest rates and the subjective probability distribution of inflation forecasts”, Journal of Money, Credit and Banking, 20, 233-248.
Laster, D., P. Bennett and I.S. Geoum (1999), “Rational bias in macroeconomic forecast”, The Quarterly Journal of Economics, 114, 293-318.
Levi, M. and J. Makin (1978), “Anticipated inflation and interest rates: Further interpretation of findings on the Fisher equation”, American Economic Review, 68, 801-812.
Lucas, R.E. (1972), “Expectations and the neutrality of money”, Journal of Economic Theory, 4, 103-124.
Lucas, R.E. (1973), “Some international evidence on output-inflation tradeoffs”, American Economic Review, 63, 326-334.
Makin, J. (1983), “Real interest, money surprises, anticipated inflation, and fiscal deficits”, Review of Economics and Statistics, 65, 374-384.
Mankiw, N.G., R. Reis and J. Wolfers (2003), “Disagreement about inflation expectation”, NBER Working Paper No. w9796.
Mankiw, N.G., R. Reis (2002), “Sticky information versus sticky prices: a proposal to replace the new Keynesian Phillips curve”, Quarterly Journal of Economics, 117, 1295-1328.
Manski, C.F. (2004), “Measuring expectations”, Econometrica, 72, 1329-1376.
McNees, S. (1989), “Why do forecasts differ”, New England Economic Review, Jan./Feb., 42-54.
Nelson, D.B. (1991), “Conditional heteroskedasticity in asset returns: a new approach”, Econometrica, 59, 347-370.
Palm, F., and A. Zellner (1992), “To combine or not to combine? Issue of combining forecasts”, Journal of Forecasting, 11, 687-701.
Rich, R. and J. Tracy (2003), “Modeling uncertainty: Predictive accuracy as a proxy for predictive confidence”, Federal Reserve Bank of New York Staff Reports, No.161.
Schwert, G.W. (1989a), “Why does stock market volatility change over time”, Journal of Finance, 44, 1115-1153.
Schwert, G.W. (1989b), “Business cycles, financial crises, and stock volatility”, Carnegie-Rochester Conference Series on Public Policy, 39, 83-126.
Sims, C. (2002), “The role of models and probabilities in the monetary policy process”, Brookings Papers on Economic Activity, 2002(2), 1-62.
Šmidková, K. (2003), “Methods available to monetary policy makers to deal with uncertainty”, paper presented at the conference “Forecasting in a Central Bank”, Bank of England, August 2003, London.
Souleles, N., (2004), “Expectations, heterogeneous forecast errors, and consumption: micro evidence from the Michigan Consumer Sentiment Surveys”, Journal of Money, Credit and Banking, 36, 39-72.
Stock, J. and M.W. Watson (1999), “Forecasting inflation”, Journal of Monetary Economics, 44, 293-335.
Stuart, A. and J.K. Ord (1994), Kendall’s advanced theory of statistics, vol1, John Wiley & Sons Inc.
Taylor, S. (1986), Modeling Financial Time Series. Wiley and Sons: New York, NY.
Wallis, K.F. (2004), “Combining density and interval forecasts: a modest proposal”, Mimeo, October 2004. University of Warwick, UK.
Zarnowitz, V. and L.A. Lambros (1987), “Consensus and uncertainty in economic prediction”, Journal of Political Economy, 95, 591-620.
Zellner, A. (1986), Bayesian estimation and prediction using asymmetric loss functions, Journal of the American StatisticalAssociation, 81, 446-451.