Confidence intervals for spectral mean and ratio statistics

Abstract

We propose a new method, to construct confidence intervals for spectral mean and related ratio statistics of a stationary process, that avoids direct estimation of their asymptotic variances. By introducing a bandwidth, a self-normalization procedure is adopted and the distribution of the new statistic is asymptotically nuisance-parameter free. The bandwidth is chosen using information criteria and a moving average sieve approximation. Through a simulation study, we demonstrate good finite sample performance of our method when the sample size is moderate, while a comparison with an empirical likelihood-based method for ratio statistics is made, confirming a wider applicability of our method.