Machine Learning and the Random Walk Puzzle: Forecasting the CAD/USD Exchange Rate with Expanding Window Evaluation and SHAP Interpretability
Summary
This paper examines whether ML models can beat the random walk benchmark in forecasting USD/CAD exchange rates, finding that only linear regression statistically outperforms the naive model, with SHAP analysis showing short-term lags dominate predictions.
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# Machine Learning and the Random Walk Puzzle: Forecasting the CAD/USD Exchange Rate with Expanding Window Evaluation and SHAP Interpretability Source: [https://arxiv.org/abs/2606.15058](https://arxiv.org/abs/2606.15058) [View PDF](https://arxiv.org/pdf/2606.15058) > 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\. ## Submission history From: Edmund Agyemang \[[view email](https://arxiv.org/show-email/e13c952d/2606.15058)\] **\[v1\]**Sat, 13 Jun 2026 02:13:18 UTC \(1,675 KB\)
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