Signals with varying periodicity frequently appear in real-world phenomena, necessitating the development of efficient modelling techniques to map the measured nonlinear timeline to linear time. Here we propose a regression model that allows for a representation of periodic and dynamic patterns observed in time series data. The model incorporates a hidden strictly increasing stochastic process that represents the instantaneous frequency, allowing the model to adapt and accurately capture varying time scales. A case study focusing on age estimation of narwhal tusks is presented, where cyclic element signals associated with annual growth layer groups are analyzed. We apply the methodology to data from one such tusk collected in West Greenland and use the fitted model to estimate the age of the narwhal. The proposed method is validated using simulated signals with known cycle counts and practical considerations and modelling challenges are discussed in detail. This research contributes to the field of time series analysis, providing a tool and valuable insights for understanding and modeling complex cyclic patterns in diverse domains.

翻译：具有变化周期性的信号在现实世界现象中频繁出现，这需要开发高效的建模技术，将测量的非线性时间线映射到线性时间。本文提出一种回归模型，该模型能够表示在时间序列数据中观察到的周期性动态模式。该模型包含一个代表瞬时频率的隐藏严格递增随机过程，使其能够适应并准确捕捉变化的时间尺度。本文展示了一个专注于独角鲸长牙年龄估计的案例研究，其中分析了与年度生长层组相关的循环元素信号。我们将该方法应用于从西格陵兰岛采集的一根此类长牙的数据，并使用拟合模型来估计该独角鲸的年龄。所提出的方法通过已知循环计数的模拟信号进行了验证，并对实际考虑因素和建模挑战进行了详细讨论。这项研究为时间序列分析领域做出了贡献，为理解和建模不同领域中复杂的循环模式提供了工具和宝贵的见解。