Abstract
Inference for statistics of a stationary time series often involves nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some of these issues. For a broad class of statistics, an orthogonal sample is constructed through a slight modification of the original statistic such that it shares similar distributional properties as the centralized statistic of interest. We use the orthogonal sample to estimate nuisance parameters of the weighted average periodogram estimators and L2‐type spectral statistics. Further, the orthogonal sample is utilized to estimate the finite sampling distribution of various test statistics under the null hypothesis. The proposed method is simple and computationally fast to implement. The viability of the method is illustrated with various simulations.
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