Time Series Forecasting Using Smoothing Ensemble Empirical Mode Decomposition and Machine Learning Techniques

Forecasting time-series is the most significant features of time-series analysis. For the time series that are non-stationary and non-linear, forecasting becomes more challenging. In this paper, a hybrid method of the smoothing ensemble empirical mode decomposition (SEEMD) and two machine-learning techniques, long short-term memory (LSTM) networks and convolutional neural networks (CNN), are evaluated for forecasting time series. The proposed forecasting method is called SEEMD-LSTM-CNN. First, the embedded signals in the time series are extracted using SEEMD. These signals called intrinsic mode functions (IMFs). Then, a combined method of LSTM network and CNN are used to predict the future IMFs and trend, from which the predicted time series can be constructed. In this study, three sets of synthetic datasets were used; these included data with linear and non-linear trends, as well as noise. The datasets were split for the purposes of training and testing the models: 70% of the data were used for training the model, and 30% to test the model. The high-frequency IMFs were predicted with $R^{2}=0.92$ and a mean absolute error (MAE) of 0.043, and the low-frequency IMFs with $R^{2}=0.99995$ and an MAE of 0.003. The proposed hybrid method produced more accurate results for the trends, with $R^{2}=0.\overline{9}9998$ and an MAE of 0.0002. In general, the proposed hybrid forecasting method was able to predict the time series with a high accuracy.

I. Introduction

Time series have a broad range of applications, including the prediction of stock prices and weather. Because of the importance of time-series prediction, numerous studies have been done to find the most efficient and accurate tool [1]. When the time series is non-linear and non-stationary, its prediction is more challenging [2], especially when rapid changes occur in the data, for example, the rapid changes in trading rules and management systems, or rapid climate change related to weather data.