## 1 Introduction  
Modeling and forecasting of time series data play a pivotal role in various industries and organizations, spanning economic, social, and environmental domains. These practices enable accurate predictions, facilitating effective prevention, control, and planning within a given area. Consequently, the development of intelligent predictive systems for time series data has garnered significant attention from the scientific community, resulting in a wealth of research publications.  
However, the challenge of achieving precise predictions and the necessity to enhance existing algorithms have made predictive models an enduring subject of research. Additionally, since each time series possesses unique characteristics, no single optimal technique exists for predicting future values. Instead, the nature of the observed variable dictates the most suitable model for a specific case.  
Thus, recent studies encompass a broad spectrum of models, ranging from simple linear approaches like autoregressive integrated moving average (ARIMA) [1; 2; 3; 4; 5; 6], seasonal ARIMA (SARIMA) [7; 8; 9; 10], and ARIMA exogenous variable models (ARIMAX) [11; 12; 13],to more sophisticated nonlinear techniques based on machine learning (ML) [14; 15; 16; 17; 18; 19; 20; 21; 22]. These advancements have paved the way for novel hybrid models that combine ARIMA linear models with a correction mechanism utilizing support vector regression (SVR), leading to successful applications across various fields [23; 24; 25; 26; 27].  
Nonetheless, both the ARIMA and ARIMA-SVR models inherit limitations from the ARIMA framework, rendering them somewhat inflexible due to their reliance on linear relationships between observed variable values [28; 29]. To overcome these limitations, the focus of autoregressive modeling has shifted towards neural networks in recent years [30; 31; 32; 33]. The advantage of neural networks over linear models lies in their ability to adapt and learn from the time series' specific circumstances, uncovering nonlinear relationships within the data. Additionally, nonlinear autoregressive (NAR) neural networks solely rely on the observed variable's information, eliminating the need for exogenous variables. Recent studies in areas such as agriculture [34; 35], economy [36], sustainability [37; 38; 39; 40], energy [41], traffic flow [42], waste management [43], SARS-CoV-2 analysis [44; 45], and other sectors [46; 47; 48; 49; 50] have demonstrated the effectiveness of NAR networks.  
Therefore, the primary aim of this study is to overcome these constraints by leveraging NAR models, which are well known for their ability to detect intricate nonlinear connections within time series data. These models adapt to a wide array of patterns through learning rules. In addition, by extending upon the methodologies employed in ARIMA-SVR models, we enhance the flexibility of this NAR model by introducing an error correction factor. This augmentation further bolsters the model's adaptability. The pivotal innovation of this study resides in the conception of NAR-SVR neural networks. These networks advance predictive capabilities by initially furnishing a forecast grounded in NAR networks, followed by posteriori corrections utilizing SVR to rectify any discrepancies in the prediction of observed variables. Although some preliminary research has explored similar concepts [51; 52; 53], no publication to date has specifically employed this algorithm on time series forecasting. To establish the generalizability of our findings, this work will compare the performance of the new model with others.  
Consequently, following the introduction, this paper describes the methodology employed and presents the datasets utilized. Subsequently, an analysis of results is conducted based on the type of neural networks employed. The paper concludes with a section comparing the obtained results with those of other published studies, proposing future research directions, and presenting the overall conclusions.