This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time. We derive results for both the theoretical setting, where we assume access to the entire process sample path, and a more practical one, which develops methods for estimating the quantities of interest from sampled time series. The latter estimates are accurately computable in reasonable time by solving the relevant linear integral equation using the iterative thresholding method due to Daubechies, Defrise and De~Mol. We exemplify our new methods by computing spectral and autocovariance estimates on irregularly-spaced heart-rate data obtained from a recent sleep-state study.

翻译：本文介绍了连续时间局部平稳小波过程这一新的类别。连续时间模型首次使我们能够为不规则间隔观测数据提供基于尺度的恰当时间序列模型。我们推导了理论设定（假设可获取完整过程样本路径）与更实际设定（开发从采样时间序列中估计感兴趣量的方法）两方面的结果。后者可通过戴比希斯、德弗里斯和德莫尔提出的迭代阈值方法求解相关线性积分方程，在合理时间内实现精确计算。我们通过计算近期睡眠状态研究中获取的不规则间隔心率数据的谱和自协方差估计，展示了新方法的应用。