Juan Antonio Bautista

Many studies report forecasting gains for sophisticated machine-learning and deep-learning models without testing whether those gains survive comparison against simple, reproducible benchmarks. This study tests that question for one-step-ahead monthly forecasting of wheat, corn, and soybean prices (FRED, 2000–2024; 300 observations, 179 training sequences). A 63-variable feature pipeline is built from MACD, RSI, Bollinger Bands, moving averages, volatility, momentum, and cross-commodity ratios. Eight learned models (SVR, Random Forest, Gradient Boosting, LSTM, GRU, Bidirectional LSTM, Attention-LSTM, and a MACD-Enhanced architecture, MADLF) are evaluated against two primary benchmarks, persistence and ARIMA (1, 1, 0), under one leakage-controlled, chronological protocol; four additional naive and statistical baselines (seasonal-naive, drift, ETS, Theta) are used for robustness. Forecast accuracy is assessed with RMSE, MAE, MASE, and Theil’s U2, and statistical significance with the Diebold–Mariano and Hansen’s SPA tests. No learned model shows statistically significant superiority over the naive benchmarks. For wheat and soybean, Diebold–Mariano tests reject all 16 learned-model comparisons; for corn, 4 of 8 are rejected against persistence and 5 of 8 against ARIMA, while Random Forest, BiLSTM, and MADLF are statistically indistinguishable from both, though with only 53 paired test observations this does not establish equivalence. Hansen’s SPA test cannot reject persistence as at least as good as the best learned model for any commodity. Descriptively, persistence attains $R^2=0.747$, $0.738$, and $0.662$ for wheat, corn, and soybean, respectively, versus $0.313$, $0.773$, and $0.399$ for the best learned model (computed from the same forecast series used for the significance tests throughout this article). Relative-skill metrics, a budget-constrained tuning check, three alternative training-window splits, a rolling-origin evaluation, and a matched-series multivariate (VAR) baseline all point to the same pattern, though the three splits and the rolling-origin check draw on a shared, overlapping 264-month timeline rather than independent samples, so they should be read as consistent rather than as independent confirmations. The recurrent architectures used here have 174,000 to 312,000 parameters but are trained on only 179 sequences; given this, the most reasonable interpretation of the null result is that simple benchmarks are hard to beat in a small-sample, monthly-data setting, not that architectural complexity is unhelpful in general. The findings are conditional on the specific feature representation, sample size, forecasting horizon, and experimental setting used in this study, and should not be read as a general claim that architectural complexity is unhelpful.

This paper develops a hybrid fractional-order framework for medium-horizon forecasting of wheat, corn, and soybean prices, combining a Caputo fractional differential equation with exogenous macro-climatic drivers (weather, crude oil, exchange rate, inflation) and a machine learning residual-correction layer. Existence, uniqueness, and Ulam–Hyers stability are established for both Caputo and Atangana–Baleanu formulations via Banach fixed-point theory, with numerical illustration through a fractional Adams–Bashforth–Moulton predictor–corrector scheme. Formal unit-root tests (ADF, KPSS, Phillips–Perron) confirm $I\left(1\right)$ behaviour in log-price levels and stationarity in first differences. Residuals are corrected using XGBoost and two feedforward neural networks (MLP-A, MLP-B), producing a family of hybrid forecasting models. Using 25 years of monthly FRED data (January 2000–December 2024), multi-method long-memory diagnostics (Hurst exponent, Lo’s modified $R/S$ test, DFA, local Whittle estimation) confirm near unit-root fractional integration in log-price levels ($H\in [0.985,1.044]$), with estimated fractional orders $\widehat{\alpha }\in \{0.737,0.884,0.451\}$ for wheat, corn, and soybean. Under a strict rolling-origin protocol (17 origins, horizons $h\in \{1,5,6,12\}$ months), conventional benchmarks remain competitive at $h=1$, but their MAPE degrades to 16.6–31.9% at $h=12$, while Frac+XGBoost error stays flat at 3.9–14.5%. This horizon-robust advantage holds across three market regimes (COVID-19 pandemic shock, 2021–2022 super-cycle, 2023–2024 normalisation) and is confirmed by Holm–Bonferroni-corrected Diebold–Mariano tests ($p<0.001$ at $h=12$). The model’s structural advantage emerges at $h\ge 5$ months, supporting procurement planning, food-security buffer stocks, and import budgeting.

This article presents the Asymmetric Cross-Market Dynamics Network (ACMD-Net), a forecasting framework built on the premise that commodity markets are fundamentally asymmetric. Three symmetry assumptions are statistically tested and rejected: volatility symmetry via the GJR-GARCH leverage test $\gamma >0$, $p<0.001$, coupling symmetry via the directional Granger causality DM statistic, 3.18–3.67, $p<0.001$, and cointegration symmetry via a likelihood ratio test, $p<0.01$. Each rejected hypothesis motivates a corresponding architectural component, yielding causally interpretable forecasts unavailable in black-box alternatives. The model is evaluated on daily CBOT futures for corn, wheat, and soybeans from January 2010 to December 2023, $T=3508$. ACMD-Net achieves RMSE reductions of 37–42% over ARIMA and 15–17% over standard LSTM. At short horizons ($h=1$), TFT achieves marginally lower point RMSE (3–4%, not statistically significant; DM $p>0.05$); at long horizons ($h=22$), TFT continues to report the lowest point RMSE across all commodities; differences versus ACMD-Net are not statistically significant DM $<1.96$ for all commodities. The architecture’s predictive value lies in economically grounded interpretability and superior directional accuracy rather than universal RMSE dominance. Directional accuracy ranges from 60 to 62% $p<0.001$, and net-positive trading returns are obtained for wheat and soybeans at 8–12-basis-point transaction costs. Ablation analysis identifies temporal attention as the primary performance driver, RMSE $+22.2\%$, upon removal, with econometric features contributing an additional 24.9% gain.