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The Behavior Of Forecast Errors From A Nearly Integrated Ar(1) Model As Both Sample Size And Forecast Horizon Become Large

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  • Kemp, Gordon C.R.

Abstract

We develop asymptotic approximations to the distribution of forecast errors from an estimated AR(1) model with no drift when the true process is nearly I(1) and both the forecast horizon and the sample size are allowed to increase at the same rate. We find that the forecast errors are the sums of two components that are asymptotically independent. The first is asymptotically normal whereas the second is asymptotically nonnormal. This throws doubt on the suitability of a normal approximation to the forecast error distribution. We then perform a Monte Carlo study to quantify further the effects on the forecast errors of sampling variability in the parameter estimates as we allow both forecast horizon and sample size to increase.

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 15 (1999)
Issue (Month): 02 (April)
Pages: 238-256

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Handle: RePEc:cup:etheor:v:15:y:1999:i:02:p:238-256_15

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Cited by:
  1. Guillaume Chevillon, 2004. ""Weak" trends for inference and forecasting in finite samples," Documents de Travail de l'OFCE 2004-12, Observatoire Francais des Conjonctures Economiques (OFCE).
  2. Hansen, Bruce E., 2010. "Averaging estimators for autoregressions with a near unit root," Journal of Econometrics, Elsevier, vol. 158(1), pages 142-155, September.
  3. Gospodinov, Nikolay, 2002. "Median unbiased forecasts for highly persistent autoregressive processes," Journal of Econometrics, Elsevier, vol. 111(1), pages 85-101, November.
  4. Helmut Luetkepohl, 2009. "Forecasting Aggregated Time Series Variables: A Survey," Economics Working Papers ECO2009/17, European University Institute.
  5. Jardet, C. & Monfort, A. & Pegoraro, F., 2009. "No-arbitrage Near-Cointegrated VAR(p) Term Structure Models, Term Premia and GDP Growth," Working papers 234, Banque de France.
  6. Ulrich Mueller & Mark W. Watson, 2013. "Measuring Uncertainty about Long-Run Prediction," NBER Working Papers 18870, National Bureau of Economic Research, Inc.
  7. Wojciech Charemza & Carlos Diaz Vela & Svetlana Makarova, 2013. "Inflation fan charts, monetary policy and skew normal distribution," Discussion Papers in Economics 13/06, Department of Economics, University of Leicester.

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