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.