We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats the coefficients as i.i.d. and estimates their prior. Asymptotically, when K is proportional to T the empirical Bayes estimator is shown to be: (i) optimal in Robbins' (1955, 1964) sense; (ii) the minimum risk equivariant estimator; and (iii) minimax in both the frequentist and Bayesian problems over a class of nonGaussian error distributions. Also, the asymptotic frequentist risk of the minimum risk equivariant estimator is shown to equal the Bayes risk of the (infeasible subjectivist) Bayes estimator in the Gaussian case, where the 'prior' is the weak limit of the empirical cdf of the true parameter values. Monte Carlo results are encouraging. The new estimators are used to forecast monthly postwar U.S. macroeconomic time series using the first 151 principal components from a large panel of predictors.
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number
0269.
Length: Date of creation: Mar 2001 Date of revision: Handle: RePEc:nbr:nberte:0269
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Find related papers by JEL classification: C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation
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James H. Stock & Mark W. Watson, 1998.
"Diffusion Indexes,"
NBER Working Papers
6702, National Bureau of Economic Research, Inc.
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James H. Stock & Mark W. Watson, 1999.
"Forecasting Inflation,"
NBER Working Papers
7023, National Bureau of Economic Research, Inc.
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