INFERENCE-WITHOUT-SMOOTHING IN THE PRESENCE OF NONPARAMETRIC AUTOCORRELATION

In a number of econometric models, rules of large-sample inference req uire a consistent estimate of f(0), where f(lambda) is the spectral de nsity matrix of y(t) = u(t) x x(t), for covariance stationary vectors u(t), x(t). Typically y(t) is allowed to have nonparametric autocorrel ation, and smoothing is used in the estimation of f(0). We give condit ions under which f(0) can be consistently estimated without smoothing. The conditions are relevant to inference on slope parameters in model s with an intercept and strictly exogenous regressors, and allow regre ssors and disturbances to collectively have considerable stationary lo ng memory and to satisfy only mild, in some cases minimal, moment cond itions. The estimate of f(0) dominates smoothed ones in the sense that it can have mean squared error of order n(-1), where n is sample size . Under standard additional regularity conditions, we extend the estim ate of f(0) to studentize asymptotically normal estimates of structura l parameters in linear simultaneous equations systems. A small Monte C arlo study of finite sample behavior is included.