The rapid emergence of the smart industry hides numerous challenges that need to be addressed promptly. In the transition between two industrial eras (Industry 4.0 and Industry 5.0), hands-on applications of digital twins in intelligent manufacturing are pivotal in enhancing efficiency, optimizing operations, and ensuring sustainability. The paper presents the digital twin (DT) concept in a vertical Industrial Internet of Things (IIoT) framework powered by machine learning (ML) models for time series forecasting. According to DT needs and hierarchical data processing, as well as edge, fog, and cloud computing, the paper presents state-of-the-art ML models and algorithms. Real-time and low-latency requirements of smart edge devices and monitoring systems force the selection of DT models powered by ML models for time series processing and forecasting. Stronger computer resources characterize the IIoT fog level. At this level, DT models should be supported by techniques and methods for parameter selection, correlation analysis, and heatmap visualization that facilitates time series processing. Special attention is devoted to developing a novel multivariate-time-series prediction method. This method should enable parameter prediction which cannot be directly measured. The method was validated based on several real-time series.