Circular data are those for which the natural support is the unit circle and its toroidal extensions. Numerous constructions have been proposed which can be used to generate models for such data. We propose a new, very general, one based on the normalization of the spectra of complex‐valued stationary processes. As illustrations of the new construction's application, we study models for univariate circular data obtained from the spectra of autoregressive moving average models and relate them to existing models in the literature. We also propose and investigate multivariate circular models obtained from the high‐order spectra of stationary stochastic processes generated using linear filtering with an autoregressive moving average response function. A new family of distributions for a Markov process on the circle is also introduced. Results for asymptotically optimal inference for dependent observations on the circle are presented which provide a new paradigm for inference with circular models. The application of one of the new families of spectra‐generated models is illustrated in an analysis of wind direction data.

中文翻译：

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时间序列频谱的圆形数据模型

圆形数据是那些自然支撑为单位圆及其环形扩展的数据。已经提出了许多可用于生成这种数据的模型的构造。我们基于复数值平稳过程的光谱归一化提出了一种新的，非常通用的方法。作为新建筑应用的说明，我们研究了从自回归移动平均模型的光谱中获得的单变量圆形数据模型，并将它们与文献中的现有模型相关联。我们还提出并研究了多元线性模型，该模型是通过使用具有自回归移动平均响应函数的线性滤波生成的平稳随机过程的高阶谱获得的。还介绍了圆上的马尔可夫过程的新分布族。提出了圆上依赖观测的渐近最优推断结果，为圆模型的推断提供了新的范例。在对风向数据的分析中说明了一种新的频谱生成模型系列的应用。