Abstract
The existing long-term time-series forecasting methods based on the neural networks suffer from multiple limitations, such as accumulated errors and diminishing temporal correlation, which compromise the prediction quality. To overcome these shortcomings, in this article, we build trend fuzzy granulation-based long short-term memory (LSTM) neural networks to carry out long-term forecasting, where data points with consistent trend characteristics, including trend change, fluctuation range, and trend persistence, are predicted in unison rather than individually. Noticing that these trend characteristics are more urgently needed than just magnitude information, a question on how to granulate a time series into a granular time series consists of meaningful granules containing trend information that comes to be a crucial step. Only if the established granules fit the varying patterns of time series at utmost, such a granulation can make sense for the improvement of the forecasting accuracy; thus, an optimization method of trend-oriented fuzzy granulation is proposed to meliorate the granulation results. With the built trend fuzzy granulation-based LSTM networks, the successive iterations of one-step forecasting are prevented, and the prediction errors of data within a granule will not further increase. This is the first attempt to build trend fuzzy granule-based LSTM to predict the trend characteristics. Experiments on publicly available time series show good performance of the proposed model.