## 1 Introduction  
The injection molding process, which is the core production method in the plastics industry and is also the most energy-intensive process, requires careful consideration of energy consumption [1]. Therefore, it is crucial to examine the opportunities for energy saving in this process [2]. A reduction in the energy consumption of the injection molding process leads to substantial energy savings for the entire industry [3, 4]. Several types of injection molding machines (IMMs) are used in the plastics industry, including hydraulic, electric, and hybrid machines. These machines differ in actuation methods used for screw rotation, injection, and clamping motions [5]. Notably, all-electric IMMs consume significantly less energy than hydraulic ones, leading to a growing trend in their usage in the plastics industry [6]. It is crucial to explore further energy-saving opportunities in all-electric IMMs because only a few studies have been conducted on this topic [7, 8, 9, 10]. Published research has primarily focused on the influence of the process parameters on the energy consumption of hydraulic IMMs [11]. Several studies have explored the impact of individual or a combination of parameters on the energy consumption of hydraulic and hybrid machines. Some studies examined the effects of motor and pump types on the energy consumption of hybrid IMMs [6]. However, it is challenging to investigate energy consumption under real operating conditions because the methodologies in the literature are insufficient to accurately capture trends and patterns over time. Data mining can provide valuable insights into trends and patterns of energy usage over time. The energy consumption profiles of the IMMs may reveal similarities based on the specific processes and products involved in one or more process cycles. An analysis of these energy consumption profiles could lead to the optimization of the process settings. Energy consumption data, expressed in kilowatt-hours (kWh) over time, constitute time-series data that can be used to evaluate energy efficiency. Clustering, which involves categorizing energy consumption patterns into groups and optimizing the similarity and dissimilarity within and between groups, has been employed to identify common patterns in energy efficiency planning [12]. A comprehensive analysis of clustering techniques and benchmark evaluation for time-series data are presented in [13] and [14], respectively. In this paper, we present a parametric model for clustering time-series data based on an underlying mixture of statistical distributions. Each distribution represents a distinct cluster and the clustering process involves assigning a mixture component (cluster) to each time series using posterior probabilities [15]. Our implementation employs mixtures of regression models, such as spline and polynomial functions of time, due to their ability to model heterogeneous time series. We selected \(K\)-means and spectral clustering algorithms as benchmark methods for our approach because of their wide availability and numerous implementations across various fields, including energy-data clustering [16; 17]. Autocorrelation, which is the relationship between the present and past values of a variable, can have a significant impact on the analysis and modeling of time-series data. Autocorrelation in data is often a natural and expected occurrence, such as in the case of energy consumption, where current consumption is influenced by previous consumption. However, autocorrelation may indicate a complex underlying process in other cases. For instance, in the case of manufacturing data, autocorrelation can be influenced by various factors including scheduling patterns, demand seasonality, and long-term trends. In the case of the plastic injection molding process, the autocorrelation of energy consumption is related to several variables, including production volume, machine settings, and raw material properties.