# Inference-Without-Smoothing in the Presence of Nonparametric Autocorrelation

https://doi.org/0012-9682(199809)66:5<1163:IITPON>2.0.CO;2-#
p. 1163-1182

P. M. Robinson

In a number of econometric models, rules of large-sample inference require a consistent estimate of f(0), where f($\lambda$) is the spectral density matrix of $y_t = u_t \otimes x_t,$ for covariance stationary vectors u$_t$, x$_t$. Typically y$_t$ is allowed to have nonparametric autocorrelation, and smoothing is used in the estimation of f(0). We give conditions under which f(0) can be consistently estimated without smoothing. The conditions are relevant to inference on slope parameters in models with an intercept and strictly exogenous regressors, and allow regressors and disturbances to collectively have considerable stationary long memory and to satisfy only mild, in some cases minimal, moment conditions. 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 estimate of f(0) to studentizeasymptotically normal estimates of structural parameters in linear simultaneous equations systems. A small Monte Carlo study of finite sample behavior is included.