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Forecasting is making a prediction based on historical data, knowledge, and experience of the related problems (Bas et al., 2014; Ghosh et al., 2016; Pala & Atici, 2019; Tai & Nghiep, 2019; Ye & Li, 2021). It is an important scientific basis for projects, policies, and development strategies. Thus, forecasting is always interested in managers and scientists. Regarding data, time series is popular in reality, and has a great demand for forecasting in many fields. For this data, two main models used for forecasting are regression and time series. The regression model has the constraints on data that are difficult to satisfy in reality, so it has the disadvantage in many cases (Efendi, et al., 2018). The time series (TS) model is used popularly in reality because it has many more advantages. For instance, auto-regression (AR) and auto-regressive integrated moving average (ARIMA) models are often applied in economy, environment, and hydrology at present (Pala & Atici, 2019; Tai & Nghiep, 2019; Tai & Thuy, 2020). However, to build the best TS model, the time series must stop, and its error must be the white noise. In addition, the data for the TS model must be linear style. These conditions are the challenges for application because they are difficult to satisfy in reality (Petneházi et al., 2019; Tai, 2019). Therefore, in many cases, the forecasting results are poor when using TS models.
In recent years, one of the research directions interested in many statisticians was to use artificial intelligence to forecast the time series. For instance, Fahim et al. (2022) explored several aspects of the application of recurrent neural networks to forecast time series. Ni Lina et al. (2019) proposed a convolutional-recurrent neural network forecasting method for time series based on deep-recurrent neural network and deep convolutional neural network, which can further improve the prediction accuracy of a traditional algorithm for the time series of the exchange rate. They fully exploited the Spatio-temporal characteristics of time series data based on the data-driven method. Pala & Atici (2019) introduced a forecasting sunspot method for time series using deep learning. Their results show that algorithms such as long-short-term memory, neural network auto-regression and deep learning algorithms perform better than classical methods such as ARIMA, Naive, and Seasonal Naive. However, they suffer from some drawbacks such as long training time and large error. To improve these disadvantages, some researchers used the fuzzy logic interference systems based on the knowledge and experience of professional experts (Robinson et al., 2021; Li et al.,2021; Yu et al., 2021). However, it was not good to forecast for the time series.