A class of circular processes based on Gaussian subordination is introduced. This allows for flexible modelling of directional time series with long‐range dependence. Based on limit theorems for subordinated processes and consistent estimation of nuisance parameters, asymptotic confidence intervals for the mean direction are derived. Extensions to cases where the direction depends on explanatory variables are also considered. Simulations and a data example illustrate the proposed method.

中文翻译：

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估计强相关循环时间序列的平均方向

介绍了一类基于高斯从属的循环过程。这允许对具有长期依赖性的定向时间序列进行灵活建模。基于从属过程的极限定理和干扰参数的一致估计，推导出平均方向的渐近置信区间。还考虑了对方向取决于解释变量的情况的扩展。模拟和数据示例说明了所提出的方法。