Applied Mathematical Forecast Evaluation of Green Bond ETF Returns Under the Random Walk Benchmark

We examine whether daily green bond exchange-traded fund (ETF) returns can be forecast more accurately than the zero-return benchmark. Using four ETFs with data through 17 April 2026, we compare linear, penalized, boosting, feedforward, recurrent, and combination forecasts in historical out-of-sample experiments. The contribution is empirical and evaluative, not a new algorithm. Combinations occasionally reduce squared error by less than 0.3%; the gains are statistically insignificant and heterogeneous across funds. An adjusted-price comparison with four conventional bond ETFs on identical dates finds no significant difference in combination-loss gains between the groups. Hyperparameter and dependence checks do not reverse these findings. Hypothetical close-to-close trading payoffs are sensitive to transaction costs, but are not executable backtests. Overall, the tested models provide limited incremental predictive information, without establishing market efficiency or a forecasting difficulty unique to green bonds.