  This paper introduces a version of empirical likelihood based on the
periodogram and spectral estimating equations. This formulation handles
dependent data through a data transformation (i.e., a Fourier transform) and is
developed in terms of the spectral distribution rather than a time domain
probability distribution. The asymptotic properties of frequency domain
empirical likelihood are studied for linear time processes exhibiting both
short- and long-range dependence. The method results in likelihood ratios which
can be used to build nonparametric, asymptotically correct confidence regions
for a class of normalized (or ratio) spectral parameters, including
autocorrelations. Maximum empirical likelihood estimators are possible, as well
as tests of spectral moment conditions. The methodology can be applied to
several inference problems such as Whittle estimation and goodness-of-fit
testing.
