Higher order asymptotic theory for nonparametric time series analysis and related contributions.

摘要: We investigate higher order asymptotic theory in nonparametric time series analysis. The aim of these techniques is to approximate the finite sample distribution estimates and test statistics. This specially relevant for smoothed presence autocorrelation, which have slow rates convergence so that inference rules based on first-order approximations may not be very precise. First we review literature autocorrelation-robust asymptotics series. evaluate effect estimation variance studentization least squares linear regression models by means expansions. Then, obtain an Edgeworth expansion spectral density studentized mean. Only local smoothness conditions spectrum are assumed, long range dependence behaviour allowed at remote frequencies, necessary only zero frequency but possible cyclical seasonal ones. methods described rely a bandwidth or smoothing number. propose cross-validation algorithm choice optimal bandwidth, mean square sense, single point without restrictions other frequencies. focus performance around singularity due their Gaussian case. Semiparametric procedures about memory parameter justified under mild observed Using fixed average periodogram ordinates, also prove consistency log-periodogram estimate non-Gaussian