經濟風險導向的殖利率曲線預測：以DV01加權為核 心的直接多步Ridge-VAR框架

Abstract

殖利率曲線的預測攸關貨幣政策與資產配置，但因橫截面維度高且可能出現狀態變遷而具挑戰性。本文建構了一套可重現的端到端預測流程，並在零息領域中進行分析與評估。在資料處理方面，首先對美國財政部的每日殖利率資料進行嚴格到期對齊，並透過具備單調（不增）及二次差分平滑條件的無套利投影，將票面殖利率轉換為折現因子與零息利率；相同的轉換亦應用於預測輸出，以確保樣本外殖利率曲線滿足無套利约束。在模型方面，以主成分分析（PCA）提取三個潛在因子，並使用 DV01 加權的 Ridge 因子重建模型重建整條殖利率曲線。核心預測模型是以因子水準（Z(t-i)）為輸入，對因子變化量（ΔZ(t,h)） 進行直接多步預測的 Ridge–VAR，其滯後階數亦由 DV01 加權的均方誤差（WMSPE）於驗證集中自動選定，使評估指標與模型選擇保持一致。此外，將核心模型與 PCA–AR 基準模型進行線性集成：在驗證期為每個預測地平線求得最適混合權重 λh⋆，並固定於測試期使用。評估方面，採用逐到期的 Diebold–Mariano（DM）檢定（包括 HLN 小樣本修正與 FDR 多重比較控制）、DV01 加權匯總的整體 DM 檢定，以及用於巢狀模型比較的 Clark–West 檢定，同時進行了 2021 年 12 月 6 日前後的事件研究。為強化對照，納入 Nelson–Siegel（DNS）、基於利率水準–斜率–曲率因子的 VAR 模型 (VAR(LSC))、隨機漫步 (RW) 等多種強力基準模型；HMM 則僅用於因子序列的敘事性分群分析。實證結果顯示，相較各項基準，核心模型在驗證期的 1 日與 5 日預測、以及測試期的 1 日預測上均實現了顯著更低的 DV01 加權誤差；而經驗證期優化的模型集成進一步提升了短期預測的精度。與 DNS、VAR(LSC) 和 RW 等模型的比較以及 Clark–West 檢定統計均嚴謹地支持了上述成果。將 PCA 替換為非線性降維的 Isomap 並未帶來樣本外表現的提升，這印證了線性三因子表示法的充分性。

Forecasting the yield curve is crucial for monetary policy and asset allocation, yet it remains challenging due to the high dimensionality of the cross-section and potential regime shifts. This paper develops a fully reproducible end-to-end forecasting pipeline operating in the zero-coupon domain. On the data side, we strictly align U.S. Treasury daily par yields across maturities and convert them into discount factors and zero rates via a no-arbitrage interpolation that enforces monotonicity and quadratic smoothness. The same transformation is applied to forecast outputs to ensure out-of-sample yield curves remain arbitrage-free. On the modeling side, three latent factors are extracted by principal component analysis (PCA), and a DV01-weighted Ridge reconstruction model is used to reconstruct the entire yield curve. The core forecasting model is a direct multi-step Ridge–VAR that uses factor levels (Z(t-i)) as predictors for future factor changes (ΔZ(t,h)), with the lag order also selected on a validation set by minimizing DV01-weighted mean squared prediction error (WMSPE), thus aligning the evaluation metric with model selection. Additionally, we form a linear ensemble of the core model with a PCA–AR benchmark: the optimal mixing weight λh⋆ for each horizon is determined on the validation period and then fixed for the test period. Evaluation includes maturity-specific Diebold–Mariano (DM) tests (with HLN small-sample adjustment and FDR control), a DV01-aggregated overall DM test, and Clark–West tests for nested comparisons, alongside an event study around December 6, 2021. Strong benchmark models—including Nelson–Siegel (DNS), a VAR on level–slope–curvature (VAR(LSC)), a random walk (RW)—are included for comparison, while an HMM on the factor series is used only for narrative regime segmentation. Empirically, the core model delivers significant DV01-weighted error reductions relative to the benchmarks at the 1-day and 5-day horizons on the validation set, and at the 1-day horizon on the test set; the validation-tuned ensemble further improves short-horizon accuracy. Comparisons against DNS, VAR(LSC), and RW baselines, along with Clark–West statistics, provide robust support for these gains. Replacing PCA with a nonlinear Isomap method yields no out-of-sample improvement, underscoring the sufficiency of a linear three-factor representation.