Empirical Bayes Forecasts of One Time Series Using Many Predictors
Thomas Knox,
James Stock and
Mark Watson
No 269, NBER Technical Working Papers from National Bureau of Economic Research, Inc
Abstract:
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.
JEL-codes: C32 E37 (search for similar items in EconPapers)
Date: 2001-03
Note: TWP
References: View references in EconPapers View complete reference list from CitEc
Citations:
Downloads: (external link)
http://www.nber.org/papers/t0269.pdf (application/pdf)
Related works:
Working Paper: Empirical Bayes Forecasts of One Time Series Using Many Predictors (2000)
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberte:0269
Ordering information: This working paper can be ordered from
http://www.nber.org/papers/t0269
Access Statistics for this paper
More papers in NBER Technical Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().