Statistical inference for quantiles in the frequency domain

For second-order stationary processes, the spectral distribution function is uniquely determined by the autocovariance function of the process. We define the quantiles of the spectral distribution function in frequency domain. The estimation of quantiles for second-order stationary processes is considered by minimizing the so-called check function. The quantile estimator is shown to be asymptotically normal. We also consider a hypothesis testing for quantiles in frequency domain and propose a test statistic associated with our quantile estimator, which asymptotically converges to standard normal under the null hypothesis. The finite sample performance of the quantile estimator is shown in our numerical studies.