Search Results (3)

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. Full article

Prediction of the economy in global markets is of crucial importance for individuals, decisionmakers, and policies. To this end, effectiveness in modeling and forecasting the directions of such leading indicators is of crucial importance. For this purpose, we analyzed the Baltic Dry Index (BDI), Investor Sentiment Index (VIX), and Global Stock Market Indicator (MSCI) for their distributional characteristics leading to proposed econometric methods. Among these, the BDI is an economic indicator based on shipment of dry cargo costs, the VIX is a measure of investor fear, and the MSCI represents an emerging and developed county stock market indicator. By utilizing daily data for a sample covering 1 November 2007–30 May 2022, the BDI, VIX, and MSCI indices are investigated with various methods for nonlinearity, chaos, and regime-switching volatility. The BDS independence test confirmed dependence and nonlinearity in all three series; Lyapunov exponent, Shannon, and Kolmogorov entropy tests suggest that series follow chaotic processes. Smooth transition autoregressive (STAR) type nonlinearity tests favored two-regime GARCH and Asymmetric Power GARCH (APGARCH) nonlinear conditional volatility models where regime changes are governed by smooth logistic transitions. Nonlinear LSTAR-GARCH and LSTAR-APGARCH models, in addition to their single-regime variants, are estimated and evaluated for in-sample and out-of-sample forecasts. The findings determined significant prediction and forecast improvement of LSTAR-APGARCH, closely followed by LSTAR-GARCH models. Overall results confirm the necessity of models integrating nonlinearity and volatility dynamics to utilize the BDI, VIX, and MSCI indices as effective leading economic indicators for investors and policymakers to predict the direction of the global economy. Full article

Under the influence of the COVID-19 pandemic and the concurrent oil conflict between Russia and Saudi Arabia, oil prices have exhibited unusual and sudden changes. For this reason, the volatilities of the West Texas Intermediate (WTI), Brent and Dubai crude daily oil price data between 29 May 2006 and 31 March 2020 are analysed. Firstly, the presence of chaotic and nonlinear behaviour in the oil prices during the pandemic and the concurrent conflict is investigated by using the Shanon Entropy and Lyapunov exponent tests. The tests show that the oil prices exhibit chaotic behavior. Additionally, the current paper proposes a new hybrid modelling technique derived from the LSTARGARCH (Logistic Smooth Transition Autoregressive Generalised Autoregressive Conditional Heteroskedasticity) model and LSTM (long-short term memory) method to analyse the volatility of oil prices. In the proposed LSTARGARCHLSTM method, GARCH modelling is applied to the crude oil prices in two regimes, where regime transitions are governed with an LSTAR-type smooth transition in both the conditional mean and the conditional variance. Separating the data into two regimes allows the efficient LSTM forecaster to adapt to and exploit the different statistical characteristics and ARCH and GARCH effects in each of the two regimes and yield better prediction performance over the case of its application to all the data. A comparison of our proposed method with the GARCH and LSTARGARCH methods for crude oil price data reveals that our proposed method achieves improved forecasting performance over the others in terms of RMSE (Root Mean Square Error) and MAE (Mean Absolute Error) in the face of the chaotic structure of oil prices. Full article