arXiv 8 Feb 2026 · Econometrics
arXiv:2602.07841 · PDF · DOI · OpenAlex · Extracted main text
This study provides a novel perspective on the metric disconnect phenomenon in financial time series forecasting through an analytical link that reconciles the out-of-sample $R^2$ ($R^2_{OOS}$) and directional accuracy (DA). In particular, using the random walk model as a baseline and assuming that sign correctness is independent of the realized magnitude, we show that these two metrics exhibit a quadratic relationship for MSE-optimal point forecasts. For point forecasts with modest DAs, the theoretical value of $R^2_{OOS}$ is intrinsically negligible. Thus, a negative empirical $R^2_{OOS}$ is expected if the model is suboptimal or affected by finite sample noise.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Christoffersen, P.F., Diebold, F.X (2006) Financial asset returns, direction-of-change forecasting, and volatility dynamics | 0.644 | 2 | 2 | 100% |
| 2 | Gu, S., Kelly, B., Xiu, D (2020) Empirical asset pricing via machine learning | 0.644 | 2 | 2 | 100% |
| 3 | Welch, I., Goyal, A (2008) A comprehensive look at the empirical performance of equity premium prediction | 0.644 | 2 | 2 | 100% |
| 4 | Petropoulos, F., Apiletti, D., Assimakopoulos, V., Babai, M.Z., Barr… (2022) Forecasting: theory and practice | 0.511 | 2 | 1 | 100% |
| 5 | Anatolyev, S., Gospodinov, N (2010) Modeling financial return dynamics via decomposition | 0.405 | 1 | 1 | 100% |
| 6 | Bollerslev, T (2023) Reprint of: Generalized autoregressive conditional heteroskedasticity | 0.405 | 1 | 1 | 100% |
| 7 | Campbell, J.Y., Thompson, S.B (2008) Predicting excess stock returns out of sample: Can anything beat the historical average? | 0.405 | 1 | 1 | 100% |
| 8 | Ellwanger, Snudden (2023) Forecasts of the real price of oil revisited: Do they beat the random walk? | 0.405 | 1 | 1 | 100% |
| 9 | Engle, R.F., Gallo, G.M (2006) A multiple indicators model for volatility using intra-daily data | 0.405 | 1 | 1 | 100% |
| 10 | Farmer, L., Schmidt, L., Timmermann, A (2023) Pockets of predictability | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 18 scored citations.