Learning a forecasting model's errors offers a modular way to improve its predictive distribution while retaining its underlying dynamics. We study this approach with Flowz, a conditional flow model of direct multi-step price-level residuals fitted using random features and ridge regression. Each EWMA, ARIMA, ARFIMA, and structural baseline is compared with a Gaussian residual location-scale control and a conditional Flowz extension. The experiment uses 24 US stocks selected across four liquidity-volatility strata, 104 common forecast origins, horizons of 5, 10, 20, 40, 80, and 160 trading observations, and three fit seeds. Marginal CRPS is the primary score. At farther horizons, Flowz reduces mean CRPS by 30.7% against EWMA and 24.0% against its Gaussian residual control. The EWMA improvement holds at each fit seed and exceeds the Gaussian control for all 24 stocks in the far band. The ARIMA, ARFIMA, and structural extensions worsen both comparators. Conditional residual learning is therefore useful for the drifting EWMA specification in this experiment, with gains concentrated at longer horizons.
🌊
