Long-term forecasting system using wavelet – nonlinear autoregressive neural network conjunction model

Abstract

Purpose An accurate long-term multi-step forecast provides crucial basic information for planning and reinforcing managerial decision-support. However, nonstationarity and nonlinearity, normally consisted of several types of managerial data can seriously ruin the forecasting computation. This paper aims to propose an effective long-term multi-step forecasting conjunction model, namely, wavelet–nonlinear autoregressive neural network (WNAR) conjunction model. The WNAR combines discrete wavelet transform (DWT) and nonlinear autoregressive neural network (NAR) to cope with such nonstationarity and nonlinearity within the managerial data; as a consequence, provides insight information that enhances accuracy and reliability of long-term multi-step perspective, leading to effective management decision-making. Design/methodology/approach Based on WNAR conjunction model, wavelet decomposition is executed for efficiently extracting hidden significant, temporal features contained in each of six benchmark nonstationary data sets from different managerial domains. Then, each extracted feature set at a particular resolution level is fed into NAR for the further forecast. Finally, NAR forecasting results are reconstructed. Forecasting performance measures throughout 1 to 30-time lags rely on mean absolute percentage error (MAPE), root mean square error (RMSE), Nash-Sutcliffe efficiency index or the coefficient of efficiency (Ef) and Diebold–Mariano (DM) test. An effect of data characteristic in terms of autocorrelation on forecasting performances of each data set are observed. Findings Long-term multi-step forecasting results show the best accuracy and high-reliability performance of the proposed WNAR conjunction model over some other efficient forecasting models including a single NAR model. This is confirmed by DM test, especially for the short-forecasting horizon. In addition, rather steady, effective long-term multi-step forecasting performances are yielded with slight effect from time lag changes especially for the data sets having particular high autocorrelation, relative against 95 per cent degree of confidence normal distribution bounds. Research limitations/implications The WNAR, which combines DWT with NAR can be accounted as a bridge for the gap between machine learning, engineering signal processing and management decision-support systems. Thus, WNAR is referred to as a forecasting tool that provides insight long-term information for managerial practices. However, in practice, suitable exogenous input forecast factors are required on the managerial domain-by-domain basis to correctly foresee and effectively prepare necessary reasonable management activities. Originality/value Few works have been implemented to handle the nonstationarity, consisted of nonlinear managerial data to attain high-accurate long-term multi-step forecast. Combining DWT and NAR capabilities would comprehensively and specifically deal with the nonstationarity and nonlinearity difficulties at once. In addition, it is found that the proposed WNAR yields rather steady, effective long-term multi-step forecasting performance throughout specific long time lags regarding the data, having certainly high autocorrelation levels across such long time lags.