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Consistent forecast intervals when the forecast‐period exogenous variables are stochastic
Author(s) -
McCullough B. D.
Publication year - 1996
Publication title -
journal of forecasting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.543
H-Index - 59
eISSN - 1099-131X
pISSN - 0277-6693
DOI - 10.1002/(sici)1099-131x(199607)15:4<293::aid-for611>3.0.co;2-6
Subject(s) - econometrics , statistics , forecast error , mathematics , variable (mathematics) , contrast (vision) , prediction interval , monte carlo method , regression , value (mathematics) , computer science , mathematical analysis , artificial intelligence
Derivation of prediction intervals in the k ‐variable regression model is problematic when future‐period values of exogenous variables are not known with certainty. Even in the most favourable case when the forecasts of the exogenous variables are jointly normal, the distribution of the forecast error is non‐normal, and thus traditional asymptotic normal theory does not apply. This paper presents an alternative bootstrap method. In contrast to the traditional predictor of the future value of the endogenous variable, which is known to be inconsistent, the bootstrap predictor converges weakly to the true value. Monte Carlo results show that the bootstrap prediction intervals can achieve approximately nominal coverage.