Machine Learning and the Random Walk Puzzle: Forecasting the CAD/USD Exchange Rate with Expanding Window Evaluation and SHAP Interpretability
Authors: Louis Agyekum, Edmund Fosu Agyemang, Obu-Amoah Ampomah, Kofi Acheampong, Emmanuel Boadi, Priscilla Yaa Amakye, Fafa Shalom Tchorly, Enock Adu Bonsu, +1 more
Organizations: Department of Economics, University of Ottawa, Ottawa, ON K1N 6N5, Canada · Department of Biostatistics and Data Science, Celia Scott Weatherhead School of Public Health and Tropical Medicine at Tulane University, New Orleans, LA 70112, USA · School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas, USA · Department of Statistics, Western Michigan University, Kalamazoo, Michigan, USA · Department of Economics, Western Michigan University, Kalamazoo, Michigan, USA · Robinson College of Business, Georgia State University, Atlanta, USA. · Department of Mathematics & Statistics, University of North Florida, Jacksonville, Florida, USA. · Department of Epidemiology and Biostatistics, University of Arizona, USA · Department of Statistics and Actuarial Science, University of Ghana, Accra, Ghana
Abstract
This study examines whether machine learning (ML) models can outperform the naive random walk benchmark in forecasting the monthly USD/CAD exchange rate. Using daily data from the Bank of Canada spanning January 2017 to May 2026, resampled into 113 monthly observations, five ML models are evaluated: linear regression, random forest, gradient boosting, XGBoost, and AdaBoost. These models are benchmarked against the naive random walk model and exponential smoothing with Holt-Winters seasonality (ETS). All models are evaluated using an expanding-window framework to maintain strict out-of-sample integrity, and forecast-accuracy differences are assessed using the Diebold-Mariano (DM) test. Structural break detection identifies four significant breakpoints in the series, corresponding to the escalation of the US-China trade war in 2018, the COVID-19 economic recovery in 2020, the peak of the Bank of Canada rate-hiking cycle in 2022, and the start of the Bank of Canada rate-cutting cycle in 2024. SHAP, or Shapley Additive Explanations, analysis is applied to interpret the drivers of the best-performing ML model. The results show that the naive random walk model remains a formidable benchmark. Linear regression is the only model that statistically outperforms the naive random walk model, with a DM statistic of 3.0585 and a p value of 0.0071, whereas the ML ensemble models show only marginal differences. Random Forest with an expanding-window framework achieves the lowest MAPE of 1.17 percent among all models except the random walk. SHAP analysis confirms that short-term lags, particularly lag1 and lag2, and recent rolling means dominate predictions, consistent with the near-random-walk behavior of exchange rates.
This paper introduces a graph-theoretic approach for predicting market regimes in foreign exchange (FX) currency prices. Specifically, the proposed model incorporates exogenous macroeconomic variables to update localized node features via message-passing operations. Utilizing the Graph Tsetlin Machine (GraphTM) framework, we empirically demonstrate the efficacy of this approach in anticipating market regimes for the US Dollar and Japanese Yen currency pair (USD/JPY). By representing multivariate macroeconomic drivers and technical indicators as hypervectorized directed multigraphs, the GraphTM leverages structured message passing to construct deep, interpretable logical clauses capable of recognizing complex sub-graph patterns.
Public health forecasts must respond to abrupt changes in surveillance data without over-extrapolating noise, reporting artifacts, or temporary trends. We evaluated autoregressive integrated moving average (ARIMA), random forest, and extreme gradient boosting (XGBoost) models using 190 weekly observations of publicly available Ontario COVID-19 case counts from January 2020 to October 2023. Rolling-origin time-series cross-validation preserved temporal order during model tuning and evaluation. Performance was assessed across three operating dimensions: responsiveness following selected turning points, forecast horizons of one to six weeks, and the amount of historical training data. We also developed Machine Learning and ARIMA Model Averaging (MLAMA), a non-negative performance-weighted ensemble with weights that vary by forecast horizon and responsiveness setting. Retrospective comparisons showed that ARIMA adapted rapidly after turning points but its normalized error increased at longer horizons. Random forest and XGBoost were less responsive initially but maintained more stable normalized error over longer horizons. For two-week forecasts at the end of the study period, training on the most recent data outperformed using longer historical periods, particularly for XGBoost. MLAMA achieved the lowest normalized mean absolute percentage error across most forecast horizons and ranked among the best-performing methods across responsiveness settings. These findings support selecting forecasting models according to operating conditions rather than relying on a single universally preferred approach. MLAMA provides a practical framework for combining complementary statistical and machine-learning forecasts. The accompanying Python package is currently maintained in a private repository while software validation and reproducibility testing are completed.
This paper investigates whether machine learning forecasts of hourly BTC-USDT returns can be converted into economically meaningful trading performance after transaction costs. Using approximately 70,000 hourly observations from 2018-2026, XGBoost, LSTM, and iTransformer are evaluated in a 27-fold walk-forward protocol. All three models produce positive gross trading performance in selected configurations, but naive sign-based strategies fail once transaction costs of ten basis points are imposed. A cost-aware execution filter, which prevents trades only when the forecast magnitude exceeds a transaction-cost-based threshold, sharply reduces turnover and restores profitability in selected configurations. The strongest long-only XGBoost strategy produces annualised returns above 65% with a Sharpe ratio above one. Additional tests show that technical indicators improve performance in selected cases, EGARCH-derived features do not provide uniformly robust gains, and XGBoost is descriptively stronger than the neural alternatives, although bootstrap evidence does not support formal statistical dominance. Loss-function and model-selection effects are secondary and statistically fragile. The results show that the main obstacle in hourly cryptocurrency trading is not only weak predictability, but also the way forecasts are converted into trades.