🤖 AI Summary
This work addresses the challenge of preserving both temporal and cross-sectional dependency structures in probabilistic forecasting of multivariate time series. To this end, the authors propose the CRAFT framework, which constructs pairs of historical backward and forward trajectories and integrates trajectory profiling, state segmentation, and conditional analogy mechanisms. By leveraging nonparametric techniques—including singular value decomposition, change-point segmentation, trajectory clustering, and a composite compatibility scoring scheme—CRAFT faithfully retains empirical dependency structures without imposing distributional assumptions. Empirical evaluation on reproducible simulation benchmarks demonstrates that CRAFT significantly outperforms competing methods such as direct analog resampling, SVD-based analogy, unconditional bootstrapping, OLS VAR bootstrapping, and random forests, thereby achieving markedly improved accuracy in multi-step probabilistic forecasts.
📝 Abstract
We propose Conditional Regime Analog Forecasting with Trajectories (CRAFT), a nonparametric framework for multivariate probabilistic time-series prediction. The method constructs paired backward and forward trajectory profiles from cumulative multi-horizon returns, learns recurrent low-dimensional regime labels in both spaces using singular value decomposition, change-point segmentation, and segment clustering, and estimates a backward-to-forward conditional regime correspondence. Forecast distributions are obtained by sampling historically realized future trajectory profiles according to a composite compatibility score that combines future-regime correspondence with similarity to the current backward trajectory profile. Unlike parametric vector autoregressions or Gaussian state-space models, CRAFT preserves empirical cross-sectional and multi-horizon dependence by resampling complete future paths. We describe the estimator, its diagnostics, and a reproducible simulation benchmark comparing CRAFT with direct analog resampling, SVD analogs, unconditional bootstrap, OLS VAR bootstrap, and random-forest forecasts.