02518cam a22002777 4500001000600000003000500006005001700011008004100028100001800069245014200087260006600229490005100295500001600346520117100362530006101533538007201594538003601666690019601702690010101898700002001999700002002019710004202039830008602081856003702167856003602204t0269NBER20160630014204.0160630s2001 mau||||fs|||| 000 0 eng d1 aKnox, Thomas.10aEmpirical Bayes Forecasts of One Time Series Using Many Predictorsh[electronic resource] /cThomas Knox, James H. Stock, Mark W. Watson. aCambridge, Mass.bNational Bureau of Economic Researchc2001.1 aNBER technical working paper seriesvno. t0269 aMarch 2001.3 aWe 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC32 - Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes • State Space Models2Journal of Economic Literature class. 7aE37 - Forecasting and Simulation: Models and Applications2Journal of Economic Literature class.1 aStock, James H.1 aWatson, Mark W.2 aNational Bureau of Economic Research. 0aTechnical Working Paper Series (National Bureau of Economic Research)vno. t0269.4 uhttp://www.nber.org/papers/t026941uhttp://dx.doi.org/10.3386/t0269