Application of a Box-Cox Transformed LSTAR-GARCH Model for Point and Interval Forecasting of Monthly Rainfall in Hainan, China

To improve the accuracy of monthly rainfall forecasting and reasonably quantify its uncertainty, this study developed a hybrid LSTAR-GARCH model incorporating a Box–Cox transformation. Using monthly rainfall data from 1999 to 2019 from four meteorological stations in Hainan Province (Haikou, Dongfang, Danzhou, and Qiongzhong), the non-stationarity and nonlinearity of the series were first verified using KPSS and BDS tests, and the Box–Cox transformation was applied to reduce skewness. A Logistic Smooth Transition Autoregressive (LSTAR) model was then established to capture nonlinear dynamics, followed by a GARCH(1,1) model to address heteroskedasticity in the residuals. The results indicate that: (1) The LSTAR model effectively captured the nonlinear characteristics of monthly rainfall, with Nash-Sutcliffe efficiency (NSE) values ranging from 0.565 to 0.802, though some bias remained in predicting extreme values; (2) While the GARCH component did not improve point forecast accuracy, it significantly enhanced interval forecasting performance. At the 95% confidence level, the average interval width (RIW) of the LSTAR-GARCH model was reduced to 0.065–0.130, substantially narrower than that of the LSTAR-ARCH model (RIW: 4.548–8.240), while maintaining high coverage rates (CR) between 93.8% and 97.9%; (3) The LSTAR-GARCH model effectively characterizes both the nonlinear mean process and time-varying volatility in rainfall series, proving to be an efficient and reliable tool for interval rainfall forecasting, particularly in tropical monsoon regions with high rainfall variability. This study provides a scientific basis for regional water resource management and climate change adaptation.