Quantile tests in frequency domain for sinusoid models

Abstract: For second order stationary processes, the spectral distribution function is uniquely deter- mined by the autocovariance functions of the processes. We define the quantiles of the spectral distribution function and propose two estimators for the quantiles. Asymptotic properties of both estimators are elucidated and the difference from the quantile estimators in time do- main is also indicated. We construct a testing procedure of quantile tests from the asymptotic distribution of the estimators and strong statistical power is shown in our numerical studies.