A novel hybrid model combining [formula omitted] and LSTM for time series forecasting

Abstract

Time series forecasting is an important and active research area due to the significance of prediction and decision-making in several applications. Most commonly used models for time series forecasting are based on Gaussianity assumption, e.g., AR (Autoregressive), ARMA (Autoregressive moving average), ARIMA (autoregressive integrated moving average), etc. But for many applications, the gaussianity presumption is too restrictive, hence non-gaussian based time series models are becoming more and more popular. Many of the hybrid models that are currently used in the literature combine ARIMA and artificial neural network (ANN) while taking various time series data into account with different approaches. Although the accuracy of the predictions made by these models is higher than that of the individual models, there is room for further accuracy improvement if the dynamics of the provided time series is taken into consideration while applying the models. In this study, a new hybrid βSARMA−LSTM model for time series forecasting is proposed. It combines a non-gaussian based time series model called Beta seasonal autoregressive moving average βSARMA with a recurrent neural network model called Long Short Term Memory Network (LSTM). The advantage of the proposed model is that βSARMA is based on the beta distribution, which contains stochastic seasonal dynamics, and LSTM is a recurrent neural network which can be used to a variety of sequential data with high levels of accuracy. In this work, a βSARMA model is applied on a given time series data in order to identify the linear structure in the data and the error between the original and βSARMA predicted data is considered as a nonlinear model, which is then modelled using LSTM. The asymptotic stability of the proposed approach is analysed to ensure that the proposed model may not show increasing variance over time. The proposed hybrid βSARMA−LSTM model along with individual ARIMA, βSARMA, LSTM, Multilayer perceptron (MLP), and some existing hybrid model ARIMA-ANN was applied on some real, simulated, and experimental datasets such as: relative humidity data, Air passengers, Bitcoin, Sunspots and Mackey Glass series. The results obtained using proposed model for all these data sets show higher prediction accuracy for both one-step and multi-step ahead forecasts.