Empirical Bayes Forecasts of One Time Series Using Many Predictors / Thomas Knox, James H. Stock, Mark W. Watson.

Format:

Book

Author/Creator:

Knox, Thomas.

Contributor:

National Bureau of Economic Research.

Stock, James H.

Watson, Mark W.

Series:

Technical Working Paper Series (National Bureau of Economic Research) no. t0269.

NBER technical working paper series no. t0269

Language:

English

Physical Description:

1 online resource: illustrations (black and white);

Place of Publication:

Cambridge, Mass. National Bureau of Economic Research 2001.

Summary:

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.

Notes:

Print version record

March 2001.