Most time series observed in practice exhibit first- as well as second-order non-stationarity. In this article we propose a novel framework for modelling series with simultaneous time-varying first- and second-order structure, removing the restrictive zero-mean assumption of locally stationary wavelet processes and extending the applicability of the locally stationary wavelet model to include trend components. We develop an associated estimation theory for both first- and second-order time series quantities and show that our estimators achieve good properties in isolation of each other by making appropriate assumptions on the series trend. We demonstrate the utility of the method by analysing the global mean sea temperature time series, highlighting the impact of the changing climate.

中文翻译：

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趋势局部平稳小波过程

在实践中观察到的大多数时间序列都表现出一阶和二阶非平稳性。在本文中，我们提出了一个新的框架，用于对具有同时时变一阶和二阶结构的序列进行建模，消除了局部平稳小波过程的限制性零均值假设，并将局部平稳小波模型的适用性扩展到包括趋势分量. 我们为一阶和二阶时间序列量开发了一个相关的估计理论，并表明我们的估计器通过对序列趋势做出适当的假设，在彼此隔离的情况下实现了良好的特性。我们通过分析全球平均海水温度时间序列来展示该方法的实用性，突出气候变化的影响。