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Estimation of the Coefficients in a Multidimensional Distributed Lag Model

Grace Wahba

Abstract

Least squares type estimates of the coefficients b(@t), @t = 0, @+ 2,..., in the general multidimensional distributed lag model Y(t) = ^@?@S"s=-@? b(s)X(t -s) + @?(t) (t = ... -1, 0, 1, ...) are considered, where {X(t)} and {Y(t)} are observable random processes @?(t) is an unobservable noise process. The asymptotic joint distribution of the estimates, conditional on the observed spectral density of the input X(t), is given, as well as the unconditional first are second moments, a readily computable confidence ellipsoid, and an approximate expression for the expected covariance in predicting Y(t) from a new realization of X(t), from a new realization of X(t), using the estimated coefficients.