A hybrid model for the time series of complex structure (HMTS) was proposed. It is based on the combination of function expansions in a wavelet series with ARIMA models. HMTS has regular and anomalous components. The time series components, obtained after expansion, have a simpler structure that makes it possible to identify the ARIMA model if the components are stationary. This allows us to obtain a more accurate ARIMA model for a time series of complicated structure and to extend the area for application. To identify the HMTS anomalous component, threshold functions are applied. This paper describes a technique to identify HMTS and proposes operations to detect anomalies. With the example of an ionospheric parameter time series, we show the HMTS efficiency, describe the results and their application in detecting ionospheric anomalies. The HMTS was compared with the nonlinear autoregression neural network NARX, which confirmed HMTS efficiency.

中文翻译：

---

具有ARIMA分量的复杂结构时间序列的混合模型

提出了一种复杂结构时间序列的混合模型（HMTS）。它基于小波系列中功能扩展与ARIMA模型的组合。HMTS具有常规和异常组件。扩展后获得的时间序列分量具有更简单的结构，如果这些分量是固定的，则可以识别ARIMA模型。这使我们能够为复杂结构的时间序列获得更准确的ARIMA模型，并扩展了应用范围。为了识别HMTS异常分量，应用了阈值函数。本文介绍了一种识别HMTS的技术，并提出了检测异常的操作。以电离层参数时间序列为例，我们展示了HMTS效率，描述了结果及其在检测电离层异常中的应用。