Efficient Semiparametric Estimation of Expectations in Dynamic Nonlinear Systems
Semiparametric estimation of the expectations of a general class of dynamic functions is considered. Such expectation functionals that are of interest for dynamic models are one- and multi-period ahead forecasting functions, distribution functions, and covariance matrices. The semiparametric efficiency bound for this problem is established and an estimator, which attains the bound is developed. The explicit form of the semiparmetric efficient expectation estimator is worked out for several explicit assumptions regarding the degree of dependence between the predetermined variables and the disturbances of the model. Under the assumption of independence, the one- and multi-period ahead residual-based predictors proposed by Brown and Mariano (1989) are shown to be semiparametric efficient. Under unconditional mean zero assumption, we propose an improved heteroskedastic autocorrelation consistent estimator.
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