This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both short- and long-memory settings. We derive some of the key probabilistic properties of periodic trawl processes and present relevant examples. Moreover, we show how such processes can be simulated and establish the asymptotic theory for their sample mean and sample autocovariances. Consequently, we prove the asymptotic normality of a (generalised) method-of-moments estimator for the model parameters. We illustrate the new model and estimation methodology in an application to electricity prices.

翻译：本文介绍了周期性拖网过程这一类连续时间、无限可分且平稳的随机过程，该过程允许周期性及灵活的序列相关形式，涵盖短记忆与长记忆设定。我们推导了周期性拖网过程的一些关键概率性质，并给出了相关实例。此外，我们展示了如何模拟此类过程，并建立了其样本均值与样本自协方差的渐近理论。由此，我们证明了模型参数的（广义）矩估计量的渐近正态性。我们通过电力价格的实际应用案例，阐述了新模型及其估计方法。