A novel two-level clustering algorithm for time series group forecasting.

Parametric models are considered the widespread methods for time series forecasting. Non-parametric or machine learning methods have significantly replaced statistical methods in recent years. In this study, we develop a novel two-level clustering algorithm to forecast short-length time series datasets using a multi-step approach, including clustering, sliding window, and MLP neural network. In first-level clustering, the time series dataset in the training part is clustered. Then, we made a long time series by concatenating the existing time series in each cluster in the first level. After that, using a sliding window, every long-time series created in the previous step is restructured to equal-size sub-series and clustered in the second level. Applying an MLP network, a model has been fitted to final clusters. Finally, the test data distance is calculated with the center of the final cluster, selecting the nearest distance, and using the fitted model in that cluster, the final forecasting is done. Using the WAPE index, we compare the one-level clustering algorithm in the literature regarding the mean of answers and the best answer in a ten-time run. The results reveal that the algorithm could increase the WAPE index value in terms of the mean and the best solution by 8.78% and 5.24%, respectively. Also, comparing the standard deviation of different runs shows that the proposed algorithm could be further stabilized with a 3.24 decline in this index. This novel study proposed a two-level clustering for forecasting short-length time series datasets, improving the accuracy and stability of time series forecasting.