## 2 Background
As opposed to parametric approaches, nonparametric approaches determine the model structure from data [22]. They include approaches such as machine learning, artificial neural networks, Gaussian mixture regression, Bayesian multivariate adaptive regression splines, and others [19; 22]. Nonparametric approaches reach very good results when using large-scale traffic data and long-term prediction [9]. Artefacts designed in this area typically use, e.g., the K-Nearest Neighbors method [30; 31; 32], support-vector machines, or regression [33; 34; 35]. Various aforementioned solutions have been compared in the literature [36; 37]. These articles have indicated better results of machine-learning approaches with tested datasets than the results of artefacts using the parametric approach (e.g., ARIMA). Despite the fact that the aforementioned nonparametric solutions are used successfully in practice, even these solutions have their limits in association with modelling complex spatiotemporal relationships and the processing of big traffic data [20; 38]. Due to this, deep learning-based approaches, which have a more complex architecture, are currently being developed. Such approaches are mainly used for short-term prediction to extract inherent knowledge of vast data. A typical solution in this area uses deep belief networks [39], long short-term memory neural networks [40], and their combination [41]. Based on literary research, it can be stated that the majority of articles containing designs of a deep learning-based solution or the comparison of these solutions have focused on a short-term prediction useful mainly for ATMS. Furthermore, the research has showed that data from a small part of the country road network (e.g., selected motorways) or, in better cases, a selected city road network, are the kind of data mainly used for testing. This article focused on the entire country (Czech Republic, a member state of the European Union) or, more precisely, all road segments for which traffic data are collected by Road and Motorway Directorate of the Czech Republic from different sensors and distributed further as real-time traffic information for the entire country (see Section 3). Another particularity of the solution introduced here is the focus on the long-term traffic speed prediction. For this purpose, historical data processed on a long-term basis was collected from various sources (e.g., concerning weather forecasts), which can help with this prediction. As the designed solution uses relatively big data (millions of records) on a long-term basis, it is still suitable to involve non-deep learning-based approaches for its processing. When designing the actual model in Section 5, the authors reflected on the benefits of using the selected parametric and nonparametric approaches due to having traffic and other types of relevant data available. In the end, the ensemble approach was selected, and the prediction model consisted of partial parametric and nonparametric submodels. The designed solution, developed primarily for advanced navigation systems in ITS, thus belongs among the already existing approaches in the area of long-term traffic speed prediction. The main benefit of the actual solution is the design of a solution concerning the problematic context set forth in Section 1.