The Development of a Hybrid Wavelet-ARIMA-LSTM Model for Precipitation Amounts and Drought Analysis

Abstract

Investigation of quantitative predictions of precipitation amounts and forecasts of drought events are conducive to facilitating early drought warnings. However, there has been limited research into or modern statistical analyses of precipitation and drought over Northeast China, one of the most important grain production regions. Therefore, a case study at three meteorological sites which represent three different climate types was explored, and we used time series analysis of monthly precipitation and the grey theory methods for annual precipitation during 1967–2017. Wavelet transformation (WT), autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) methods were utilized to depict the time series, and a new hybrid model wavelet-ARIMA-LSTM (W-AL) of monthly precipitation time series was developed. In addition, GM (1, 1) and DGM (1, 1) of the China Z-Index (CZI) based on annual precipitation were introduced to forecast drought events, because grey system theory specializes in a small sample and results in poor information. The results revealed that (1) W-AL exhibited higher prediction accuracy in monthly precipitation forecasting than ARIMA and LSTM; (2) CZI values calculated through annual precipitation suggested that more slight drought events occurred in Changchun while moderate drought occurred more frequently in Linjiang and Qian Gorlos; (3) GM (1, 1) performed better than DGM (1, 1) in drought event forecasting.

Hybrid Model for Time Series of Complex Structure with ARIMA Components

“…As a rule, time series of empirical data have a complex non-stationary structure and contain local features of various forms. The methods for the time series analysis include deterministic [11], stochastic [12][13][14] approaches and their various combinations [15][16][17][18][19]. Traditional methods for data time series modeling and analysis (AR models, ARMA [20,21], exponential smoothing [22], stochastic approximation [13], etc.)…”

“…do not allow us to describe the time series of complex structure adequately [23]. At present, hybrid approaches [16,17,19,[23][24][25][26][27][28] are widely applied. They make it possible to improve the efficiency of the procedure of data analysis in case of its complicated structure.…”

“…If these assumptions are not satisfied, the model accuracy is significantly reduced. In order to improve the ARIMA efficiency, a number of papers [16,17,26,27,34,35] suggested a hybrid approach to the time series analysis. For example, the paper [17] proposed to apply ARIMA together with discrete wavelet transform and neural network LSTM.…”

“…In order to improve the ARIMA efficiency, a number of papers [16,17,26,27,34,35] suggested a hybrid approach to the time series analysis. For example, the paper [17] proposed to apply ARIMA together with discrete wavelet transform and neural network LSTM. The authors of the paper [17] showed that the combination of ARIMA and LSTM with a discrete wavelet transform allowed them to improve the accuracy of ARIMA and LSTM models in order to make forecasts of a monthly precipitation time series.…”

“…For example, the paper [17] proposed to apply ARIMA together with discrete wavelet transform and neural network LSTM. The authors of the paper [17] showed that the combination of ARIMA and LSTM with a discrete wavelet transform allowed them to improve the accuracy of ARIMA and LSTM models in order to make forecasts of a monthly precipitation time series. A combination of the discrete wavelet transform with ARIMA and neural network was also proposed in [35] to forecast a hydrological time series.…”