Empirical Bayes procedures in time series analysis

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Virginia Polytechnic Institute and State University


Empirical Bayes analysis concerns the analysis of data which occur in similar recurring situations. The parameters involved in the recurring situations are generated independently from an unknown probability distribution G(θ). In many situations it is possible to use the estimates of all of the past parameter values to construct an estimate which reduces the mean squared error of the usual estimate of the present value of the parameter.

This dissertation involves the empirical Bayes estimates of various time series parameters: the auto-regressive time series model, the time series regression model with auto-correlated errors and the spectral density function. In each case, empirical Bayes estimators are obtained using asymptotic or approximate distributions of the usual estimators. The Parzen, Tukey and Bartlett smoothing coefficients are all used in the estimation of the spectral density function. Each estimator is tested on a high speed computer using Monte Carlo procedures.

It was found that in every situation the empirical Bayes estimators produced smaller mean squared errors than the usual estimator.