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REVIEW 4 major objections 5 minor 45 references

Regression and Forecasting of U.S. Stock Returns Based on LSTM

T0 review · 4 major / 5 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper claims that the Fama-French five-factor model is the best linear specification for all three U.S. stock sectors studied, and that an LSTM neural network predicts high-technology sector returns better than any factor model.

desk verdict Routine factor-model comparison undercut by comparing in-sample fits to out-of-sample LSTM and by vanishing LSTM implementation detail. read the letter →

arxiv 2502.05210 v3 pith:KGALFERD submitted 2025-02-03 q-fin.ST cs.LG

Shicheng Zhou , Zizhou Zhang , Rong Zhang , Yuchen Yin , Chia Hong Chang , Qinyan Shen This is my paper · ORCID
classification q-fin.STcs.LG
keywords Fama-Frenchfive-factormodelLSTMstockpredictionfactormodelssectorreturnsUSmarketmachinelearningfinanceR-squaredcomparison
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to test whether three standard factor models—the Fama-French three-factor, Carhart four-factor, and Fama-French five-factor models—explain monthly returns in three U.S. stock sectors (Manuf, Hitec, Other), and whether a long short-term memory (LSTM) network adds predictive power beyond them. It claims the five-factor model is the strongest linear specification in every sector, with R-squared values of 0.909, 0.871, and 0.946 respectively. The LSTM achieves a higher R-squared than the five-factor model only in the high-technology sector (0.929 vs 0.871). The paper's conclusion is a sector-specific recommendation: rely on the five-factor model for Manuf and Other, and combine it with LSTM for Hitec. The broader point is that linear factor models and deep learning can be complementary in forecasting stock returns.

What carries the argument

The comparison runs on two kinds of machinery: ordinary least squares regressions of excess returns on the standard factor sets (market, size, value, and for the five-factor model also profitability and investment), and an LSTM recurrent neural network with gated memory units. The factor regressions produce the estimating equations (5)-(7) and the R-squared/RMSE/MAE benchmarks in Tables 5-7. The LSTM, trained on 70 percent of the monthly data and tested on 30 percent, produces Table 8. The paper's inference about LSTM's edge in Hitec rests on reading the two sets of R-squared values side by side.

What would settle it

Re-estimate the five-factor model on the same 70 percent training window used for the LSTM and compute its R-squared on the 30 percent test window for the Hitec sector. If that out-of-sample R-squared reaches or exceeds the LSTM's 0.929, the paper's central claim fails. A supporting check is to run a walk-forward comparison across subperiods to see whether the LSTM advantage is stable or an artifact of the single split.

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Extended reading notes

Core claim

The central discovery is that the Fama-French five-factor model is the most valid of the three linear factor models for all three sectors, and that an LSTM network can capture sector-specific, nonlinear return drivers that the five-factor model misses, most clearly in high technology. For Manuf and Other, the five-factor model already explains over 90 percent of return variation, so the paper argues that more complexity buys little. For Hitec, the LSTM's R-squared of 0.929 versus the five-factor model's 0.871 is presented as evidence that neural networks can improve prediction when linear factors fall short, due to LSTM's ability to model long-term dependencies and nonlinear patterns.

Load-bearing premise

The load-bearing premise is that the full-sample R-squared of the factor models and the holdout R-squared of the LSTM are directly comparable; if they are not, the claimed LSTM superiority in high technology is not established.

Editorial extensions

If this is right

  • For the Manuf and Other sectors, the five-factor model should remain the default tool, since it explains more than 90 percent of return variation.
  • In the Hitec sector, predictions from an LSTM can exceed the five-factor model's accuracy, supporting a hybrid approach there.
  • The insignificance of RMW and CMA in the Manuf sector suggests that a leaner model may suffice for manufacturing stocks.
  • Combining factor models with LSTM offers a practical path that balances interpretability with nonlinear predictive power.
  • The results imply that the value of deep learning in return forecasting is sector-dependent, not universal.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The R-squared comparison mixes evaluation protocols: factor regressions use the full sample while LSTM uses a holdout, so the reported gap in Hitec may overstate LSTM's true advantage; an equal-protocol test is a natural extension.
  • The paper recommends substituting future SMB, HML, RMW, and CMA values into its equations, but provides no way to forecast these factors; adding a factor-forecasting module would make the recommendation actionable.
  • A walk-forward validation that retrains the LSTM and re-estimates factor betas on rolling windows would test whether the Hitec edge persists out of sample or reflects memorization of the 2004-2024 period.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The manuscript analyzes monthly U.S. stock returns for three sectors (Manuf, Hitec, Other) over January 2004 to January 2024, fitting the Fama-French three-factor, Carhart four-factor, and Fama-French five-factor regressions and an LSTM regression model. It reports R-squared, RMSE, and MAE for each model and concludes that the Fama-French five-factor model has better validity for all three sectors, while the LSTM model better predicts returns in the Hitec sector. The paper recommends using the five-factor model for Manuf and Other, and combining LSTM for Hitec.

Significance. If the comparison were valid, the paper would offer evidence on sector-specific performance differences between classical factor models and an LSTM for U.S. stock returns. The topic is relevant and the use of standard factor definitions is sensible. However, the execution prevents the results from being interpretable: the factor-model and LSTM metrics are not computed under a common evaluation protocol, the LSTM is not described sufficiently for reproduction, and the proposed forecasting procedure for the factor model is incomplete. The paper does not provide code, data, or enough methodological detail to assess whether the central claims are supported.

major comments (4)
  1. [§3.1, Tables 5–7 vs. §3.2, Table 8] The R-squared values in Tables 5–7 are in-sample fits from OLS regressions on the full 2004–2024 sample, whereas the LSTM in §3.2 is trained on 70% of the data and evaluated on the remaining 30%. If Table 8 reports test-set R-squared, then the two sets of R-squared values are not directly comparable, and the comparison is biased against the LSTM (or in favor of the factor models, depending on the direction of overfitting). The paper must compute factor-model R-squared, RMSE, and MAE on the same 30% hold-out, or report LSTM training-set performance, before any claim such as 'the Fama-French five-factor model has better validity' or 'LSTM better predicts Hitec' can be assessed.
  2. [§3.1.3, after Eq. (7)] The sentence instructing an investor to substitute predicted future values of SMB, HML, RMW, and CMA into the fitted regression presupposes that these factor values can be forecast. No method, model, or validation for forecasting these factors is provided, and no ex-ante availability argument is given. Without such a method, Equations (5)–(7) are in-sample fitted relationships rather than forecasting equations, so the investment-strategy recommendation in §4 is not supported.
  3. [§3.2, Table 8] The LSTM model is unspecified: the text does not report the input features, sequence length or lookback, number of layers, hidden units, activation functions, optimizer, learning rate, batch size, epochs, regularization, or whether the R-squared is computed on the training set or the test set. Without this information, the reported R-squared values, including the high Hitec value of 0.929, cannot be reproduced or audited for data leakage or overfitting. This is a load-bearing gap because the paper's only evidence for the LSTM claim is Table 8.
  4. [§3.1, Tables 5–7] The conclusion that the Fama-French five-factor model is 'best' rests on small in-sample R-squared differences (e.g., Manuf: 0.901, 0.904, 0.909; Hitec: 0.864, 0.864, 0.871; Other: 0.936, 0.940, 0.946) with no statistical test of whether the increments are significant, and no adjusted R-squared or out-of-sample comparison. In the Manuf regression, RMW and CMA are insignificant (p = 0.420 and p = 0.859 in Table 4), yet Equation (5) still includes them and the model is recommended. The paper should report incremental F-tests, adjusted R-squared, and cross-validated predictive comparisons before making the superiority claim.
minor comments (5)
  1. [§2.2 and §3.1.1] Equations (2)–(4) omit the intercept term even though the general regression form in Equation (1) includes β0, and Equation (4) and Equation (5) use 'MB' where 'SMB' is intended; this notation inconsistency should be corrected.
  2. [Abstract] The abstract contains a duplicated phrase: 'French five-factor model for the three sectors of the market' appears twice in consecutive sentences.
  3. [§4] The 'Investment Strategy' paragraph is repeated verbatim twice in the conclusion; one copy should be removed.
  4. [§2.4] The description of data preprocessing is vague: the paper states that vacant values are filled using Lagrange interpolation and outliers are eliminated 'in a similar way,' but it does not define the outlier criterion, the interpolation window, or the source and construction of the sector return series. More detail is needed for reproducibility.
  5. [References] Several references appear unrelated to the claims they are attached to (e.g., references [12], [13], [14], and [17] concern generalized linear models, regression modeling strategies, weighted log-rank tests, and local regression, none of which is actually used in the paper). The citation list should be trimmed to relevant sources.

Circularity Check

1 steps flagged · score 6.0 of 10

The central F-F5-versus-LSTM comparison compares an in-sample R² (Tables 5–7) with a test-set R² (Table 8), so the claimed predictive-accuracy ranking is forced by the estimation protocol rather than by out-of-sample prediction.

  1. fitted input called prediction [Section 3.1 (Tables 5–7), Section 3.2 (Table 8), and discussion after Table 8]
    "In terms of explanatory power and predictive accuracy, the F-F5 model performs the best. Using LSTM for regression on relevant data, with the training set and test set split in a 7:3 ratio. In the cases of the Manufacturing and Other sectors, if the five-factor model already has a coefficient of determination over 0.9, further use of LSTM may not significantly enhance predictive performance."

    The F-F5 R² values in Tables 5–7 come from OLS regressions fit on the full 2004–2024 sample (equations 2–7), so those R² values measure in-sample fit: OLS minimizes the sum of squared residuals on exactly the data used to compute R². The paper calls this 'predictive accuracy' and uses it to conclude that F-F5 is superior in Manuf and Other and that LSTM adds value only in Hitec. Table 8's LSTM R² is, by the 7:3 split stated in §3.2, a test-set statistic. Comparing a fit statistic to a test statistic is not a prediction: the apparent advantage of F-F5 in Manuf/Other is an artifact of reporting in-sample R², and the claimed superiority ranking is not supported. This is the load-bearing evidence for the paper's central comparative conclusion.

full rationale

The LSTM evaluation itself is genuinely out-of-sample (7:3 split), so it is not circular. The factor-model regressions are standard in-sample OLS fits; reporting R² as explanatory power would be legitimate. The circular/forced element is the paper's step of labeling those in-sample R² values 'predictive accuracy' and comparing them with the LSTM test-set R² to decide where LSTM helps. Because the F-F5 R² is by construction a measure of fit to the estimation sample, the conclusion that F-F5 is the best predictor in Manuf and Other, and that LSTM only helps in Hitec, is statistically forced by the evaluation protocol rather than derived from comparable forecasts. The paper also recommends substituting forecasted SMB, HML, RMW, and CMA values without providing a forecasting method; this is an incompleteness/correctness concern rather than a circularity. The self-citations in the reference list (e.g., [4], [5], [10], [16], [45]) are motivational and are not load-bearing for the derivation, so they do not affect the circularity score.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claims rest entirely on fitted factor loadings, an unspecified LSTM configuration, and the assumption that the data and evaluation are clean. There are no invented entities, but the model comparison depends on matching evaluation protocols that the paper does not provide.

free parameters (7)
  • FF3 loadings (Manuf) = market 0.9219, SMB 0.0473, HML 0.033
    OLS coefficients in equation (2), fitted to the full sample.
  • Carhart4 loadings (Manuf) = market 0.905, SMB 0.05, HML 0.009, MOM -0.06
    OLS coefficients in equation (3).
  • FF5 loadings (Manuf) = market 0.95, SMB 0.08, HML 0.02, RMW 0.1, CMA 0.01
    OLS coefficients in equation (4); RMW and CMA are statistically insignificant.
  • FF5 loadings (Hitec) = market 0.9, SMB 0.02, HML -0.19, RMW -0.08, CMA -0.06
    OLS coefficients in equation (6).
  • FF5 loadings (Other) = market 0.83, SMB -0.03, HML 0.2977, RMW -0.1, CMA -0.07
    OLS coefficients in equation (7).
  • Train/test split ratio = 0.7
    The LSTM uses a 70/30 split in Section 3.2; the choice affects reported test R-squared.
  • LSTM architecture and hyperparameters = not reported
    No architecture, number of layers, hidden units, learning rate, optimizer, epochs, or random seed is given in Section 3.2.
assumptions (5)
  • standard math Standard OLS assumptions hold for the factor model regressions
    The paper reports p-values and R-squared from multiple linear regression in Section 2.2 without diagnostics for linearity, heteroskedasticity, or autocorrelation.
  • domain assumption Fama-French and Carhart factor returns are correctly aligned with the sector portfolios
    Section 2.4 does not specify the factor data source; the regressions in equations (2)-(7) require SMB, HML, RMW, CMA, and MOM series.
  • domain assumption The LSTM feature set and preprocessing avoid look-ahead bias
    Section 3.2 reports LSTM R-squared but gives no feature construction, normalization, or leakage controls.
  • ad hoc to paper Future factor values can be forecasted when applying the fitted regression for prediction
    Section 3.1.3 tells investors to substitute predicted SMB, HML, RMW, and CMA into the fitted equation, but the paper provides no factor forecasting method.
  • ad hoc to paper Outlier elimination and interpolation do not materially change the results
    Section 2.4 removes outliers and fills missing values without reporting thresholds or robustness checks.

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Cite this review

Pith. "Pith review of Regression and Forecasting of U.S. Stock Returns Based on LSTM." pith.science (2026). https://pith.science/paper/KGALFERD

@misc{pith2026250205210,
  author       = {Pith},
  title        = {Pith review of: Regression and Forecasting of U.S. Stock Returns Based on LSTM},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KGALFERD}},
  note         = {Machine review of arXiv:2502.05210}
}
read the original abstract

This paper analyses the investment returns of three stock sectors, Manuf, Hitec, and Other, in the U.S. stock market, based on the Fama-French three-factor model, the Carhart four-factor model, and the Fama-French five-factor model, in order to test the validity of the Fama-French three-factor model, the Carhart four-factor model, and the Fama-French five-factor model for the three sectors of the market. French five-factor model for the three sectors of the market. Also, the LSTM model is used to explore the additional factors affecting stock returns. The empirical results show that the Fama-French five-factor model has better validity for the three segments of the market under study, and the LSTM model has the ability to capture the factors affecting the returns of certain industries, and can better regress and predict the stock returns of the relevant industries. Keywords- Fama-French model; Carhart model; Factor model; LSTM model.

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Reference graph

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Reviewed August 9, 2026 · model on record in the stance chip above.