Real time series sometimes exhibit various types of “irregularities”: missing observations, observations collected not regularly over time for practical reasons, observation times driven by the series itself, or outlying observations. However, the vast majority of methods of time series analysis are designed for regular time series only. A particular case of irregularly spaced time series is that in which the sampling procedure over time depends also on the observed values. In such situations, there is stochastic dependence between the process being modelled and the times of the observations. In this work, we propose a model in which the sampling design depends on all past history of the observed processes. Taking into account the natural temporal order underlying available data represented by a time series, then a modelling approach based on evolutionary processes seems a natural choice. We consider maximum likelihood estimation of the model parameters. Numerical studies with simulated and real data sets are performed to illustrate the benefits of this model-based approach.

实时序列有时会表现出各种类型的“不规则性”：缺失的观测值，出于实际原因不定期收集的观测值，由序列本身驱动的观测时间或偏远的观测值。但是，大多数时间序列分析方法仅适用于常规时间序列。不规则间隔时间序列的一种特殊情况是，随时间推移的采样过程也取决于观测值。在这种情况下，建模过程与观察时间之间存在随机依赖关系。在这项工作中，我们提出了一个模型，其中的抽样设计取决于观察到的过程的所有过去历史。考虑到以时间序列表示的可用数据所基于的自然时间顺序，那么基于进化过程的建模方法似乎是自然的选择。我们考虑模型参数的最大似然估计。进行了带有模拟和真实数据集的数值研究，以说明这种基于模型的方法的好处。