Bibliography

Paper SSOT for factrix. Every reference cited from a metric docstring, the Statistical methods reference page, or the design-notes page in Development lives here once, with an explicit anchor that mkdocs-autorefs resolves into reference-style links such as [Newey-West 1987][newey-west-1987].

Sections are organised by methodological role rather than chronology. Within a section, ordering follows topical relevance to the implementation rather than alphabetical author order.

Time-series regression and heteroskedasticity-and-autocorrelation-consistent (HAC) inference¶

Newey & West (1987)¶

Newey, W. K. & West, K. D. (1987). "A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix." Econometrica 55(3), 703–708.

Bartlett-kernel HAC variance estimator; underlies every Newey-West (NW) HAC t-test in factrix.

Newey & West (1994)¶

Newey, W. K. & West, K. D. (1994). "Automatic Lag Selection in Covariance Matrix Estimation." Review of Economic Studies 61(4), 631–653.

Data-adaptive plug-in bandwidth selection. Cited as background; factrix uses the simpler Andrews (1991) Bartlett growth rate \(\lfloor T^{1/3} \rfloor\) floored against the Hansen-Hodrick overlap rule.

Andrews (1991)¶

Andrews, D. W. K. (1991). "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation." Econometrica 59(3), 817–858.

Optimal Bartlett growth rate \(T^{1/3}\); the basis of factrix's default NW lag rule.

Andrews & Monahan (1992)¶

Andrews, D. W. K. & Monahan, J. C. (1992). "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator." Econometrica 60(4), 953–966.

Prewhitening refinement to NW HAC; cited as background, not implemented (factrix keeps the unprewhitened Bartlett kernel for deterministic lag selection).

Hansen & Hodrick (1980)¶

Hansen, L. P. & Hodrick, R. J. (1980). "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis." Journal of Political Economy 88(5), 829–853.

K-period forecast residuals carry MA(K−1) structure under non-overlapping innovations. Underpins two pieces of factrix's HAC machinery: (i) a standalone rectangular-kernel HAC SE estimator on sample means, available to callers who prefer an overlap-targeted rectangular kernel over the Bartlett kernel; (ii) the h−1 lag floor that factrix combines with the Andrews rule when running NW HAC under overlapping forward returns.

Hodrick (1992)¶

Hodrick, R. J. (1992). "Dividend Yields and Expected Stock Returns: Alternative Procedures for Inference and Measurement." Review of Financial Studies 5(3), 357–386.

Reverse-regression t-statistic for long-horizon return predictability with persistent regressors. The "1B" form solves the size distortion of NW / Hansen-Hodrick (1980) under heavy overlap (h / T not small) by re-expressing the long-horizon regression as a one-period regression on a moving-average of the predictor — the test statistic is then size-correct in finite samples even when the implied MA(h−1) overlap is severe.

Cited as background. Hodrick 1B reformulates the long-horizon regression as a one-period regression of r_{t,t+1} on the predictor sum X_t = Σ_{j=0}^{h-1} x_{t-j}, swapping which side carries the moving average. The coefficient has a different interpretation than the standard r_{t,t+h} ~ x_t slope, and factrix prefers non-overlapping resampling on the Individual × Continuous cell as the literature-standard mitigation for overlap-driven size distortion. See Statistical methods § HAC SE for the comparison among NW / HH-1980 / Hodrick-1992.

White (1980)¶

White, H. (1980). "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity." Econometrica 48(4), 817–838.

HC0 sandwich estimator; the heteroskedasticity-only ancestor of NW HAC. Cited as background.

Hansen (1982)¶

Hansen, L. P. (1982). "Large Sample Properties of Generalized Method of Moments Estimators." Econometrica 50(4), 1029–1054.

GMM framework and the over-identifying-restrictions J-statistic; underlies factrix's two-step efficient GMM moment-estimator path.

Cross-section and panel pricing¶

Treynor & Black (1973)¶

Treynor, J. L. & Black, F. (1973). "How to Use Security Analysis to Improve Portfolio Selection." Journal of Business 46(1), 66–86.

Original derivation of the alpha-over-residual-risk appraisal-ratio optimisation for active management — the single-asset appraisal ratio that Grinold (1989) later generalised across many independent bets to derive the \(\mathrm{IR} \approx \mathrm{IC} \times \sqrt{\mathrm{breadth}}\) identity. Conceptual ancestor of the breadth decomposition; the identity itself is Grinold's, not Treynor-Black's.

Grinold (1989)¶

Grinold, R. C. (1989). "The Fundamental Law of Active Management." Journal of Portfolio Management 15(3), 30–37.

\(\mathrm{IR} \approx \mathrm{IC} \times \sqrt{\mathrm{breadth}}\); motivates information coefficient (IC) as the canonical signal-quality measure and IR/ICIR as its time-stability normalisation.

Grinold & Kahn (2000)¶

Grinold, R. C. & Kahn, R. N. (2000). Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk (2nd ed.). McGraw-Hill.

Textbook treatment of IC, IR, breadth, and active-management diagnostics that factrix implements at the metric layer.

Fama & MacBeth (1973)¶

Fama, E. F. & MacBeth, J. D. (1973). "Risk, Return, and Equilibrium: Empirical Tests." Journal of Political Economy 81(3), 607–636.

Two-stage λ procedure: per-date cross-sectional regression then time-series t-test on E[λ]. The FM cell uses this with NW HAC at stage 2.

Black, Jensen & Scholes (1972)¶

Black, F., Jensen, M. C. & Scholes, M. (1972). "The Capital Asset Pricing Model: Some Empirical Tests." In Jensen, M. (ed.), Studies in the Theory of Capital Markets. Praeger.

Beta-sorted-portfolio time-series test of the zero-beta CAPM: sort assets into beta-ranked portfolios, then run a time-series regression of each portfolio's excess return on the market. The contribution is the time-series-then-cross-section aggregation order (per-asset / per-portfolio time series first, then cross-asset inspection) that factrix's common_continuous cell adopts; factrix's cross-asset \(t\)-test on the mean of per-asset β is a simplified analogue of this aggregation order rather than a replication of BJS's grouped-portfolio intercept test.

Petersen (2009)¶

Petersen, M. A. (2009). "Estimating Standard Errors in Finance Panel Data Sets: Comparing Approaches." Review of Financial Studies 22(1), 435–480.

Comparison of FM, clustered, and two-way SE under firm/time correlation; supports FM + Newey-West as the default for time-effect panels and motivates the two-way (date+asset) clustered SE option in factrix's FM pooled-OLS path.

Cameron, Gelbach & Miller (2011)¶

Cameron, A. C., Gelbach, J. B. & Miller, D. L. (2011). "Robust Inference With Multiway Clustering." Journal of Business & Economic Statistics 29(2), 238–249.

Two-way clustering formula V_AB = V_A + V_B − V_{A∩B}; backs the date+asset two-way clustered SE option in factrix's FM pooled-OLS path and the standalone two-way-cluster Wald estimator.

Thompson (2011)¶

Thompson, S. B. (2011). "Simple Formulas for Standard Errors that Cluster by Both Firm and Time." Journal of Financial Economics 99(1), 1–10.

Finite-sample correction df = min(G_A, G_B) − 1 used in factrix's two-way clustered SE path.

Shanken (1992)¶

Shanken, J. (1992). "On the Estimation of Beta-Pricing Models." Review of Financial Studies 5(1), 1–33.

Errors-in-variables correction for the Fama-MacBeth stage-2 \(t\)-stat when the stage-1 regressor is itself an estimated quantity (rolling \(\beta\), PCA score, ML predictor). Applied to the FM stage-2 SE in factrix's FM path when the stage-1 regressor is itself estimated. The general multi-factor multiplicative term \(1 + \lambda'\Sigma_f^{-1}\lambda\) collapses to \(1 + \hat\lambda^2/\sigma^2_f\) in the single-factor case factrix implements; factrix's simplification additionally drops the full variance's additive \(+\sigma^2_f/T\) term and is therefore honest only for large \(T\).

Kan & Zhang (1999)¶

Kan, R. & Zhang, C. (1999). "Two-Pass Tests of Asset Pricing Models with Useless Factors." Journal of Finance 54(1), 203–235.

Useless-factor diagnostics for two-pass cross-sectional tests: weak or unidentified factors yield spuriously significant Fama-MacBeth \(t\)-stats on risk premia even when the factor has no true pricing power. Cautionary background on factor validity in factrix's Fama-MacBeth path, separate from the errors-in-variables sampling-error correction (which is the Shanken (1992) single-factor case that factrix's estimated-factor correction implements).

Fama & French (1992)¶

Fama, E. F. & French, K. R. (1992). "The Cross-Section of Expected Stock Returns." Journal of Finance 47(2), 427–465.

Empirical anchor for size and value as cross-sectional risk premia; prototypical Individual × Continuous factor study in the Fama-MacBeth tradition.

Fama & French (1993)¶

Fama, E. F. & French, K. R. (1993). "Common Risk Factors in the Returns on Stocks and Bonds." Journal of Financial Economics 33(1), 3–56.

Three-factor model; prototypical multi-factor spanning baseline of the kind that factrix's spanning-alpha procedure evaluates a candidate factor against.

Event study¶

Brown & Warner (1985)¶

Brown, S. J. & Warner, J. B. (1985). "Using Daily Stock Returns: The Case of Event Studies." Journal of Financial Economics 14(1), 3–31.

Simulation framework against which event-study tests are evaluated. The cross-sectional t on CAAR is reasonably specified at moderate K under no event-induced variance and is mis-specified under variance inflation around the event date — the BW1985 documentation of this failure is the motivation for the Boehmer-Musumeci-Poulsen 1991 standardised AR test that factrix implements.

Brown & Warner (1980)¶

Brown, S. J. & Warner, J. B. (1980). "Measuring Security Price Performance." Journal of Financial Economics 8(3), 205–258.

Earlier monthly-frequency precursor; cited as background for the mean-adjusted return convention.

Fama, Fisher, Jensen & Roll (1969)¶

Fama, E. F., Fisher, L., Jensen, M. C. & Roll, R. (1969). "The Adjustment of Stock Prices to New Information." International Economic Review 10(1), 1–21.

Founding event-study paper; cited as historical anchor for the individual_sparse cell's lineage.

MacKinlay (1997)¶

MacKinlay, A. C. (1997). "Event Studies in Economics and Finance." Journal of Economic Literature 35(1), 13–39.

Standardised event-window / estimation-window vocabulary; followed by factrix's event-configuration schema.

Campbell, Lo & MacKinlay (1997)¶

Campbell, J. Y., Lo, A. W. & MacKinlay, A. C. (1997). The Econometrics of Financial Markets. Princeton University Press.

Textbook treatment of event-study test statistics; cited for the path-excursion / horizon-scaling vocabulary that factrix's MFE / MAE path-excursion metric adopts.

Boehmer, Musumeci & Poulsen (1991)¶

Boehmer, E., Musumeci, J. & Poulsen, A. B. (1991). "Event-study Methodology Under Conditions of Event-induced Variance." Journal of Financial Economics 30(2), 253–272.

BMP standardised AR test. factrix's implementation is a BMP-style variant using mean-adjusted (not market-model) abnormal returns; the prediction-error variance correction \(\sigma_i \sqrt{1 + 1/T_{\mathrm{est}}}\) of the original BMP formulation is opt-in and off by default, so default-setting results will not match a textbook BMP byte-for-byte.

Patell (1976)¶

Patell, J. M. (1976). "Corporate Forecasts of Earnings Per Share and Stock Price Behavior: Empirical Tests." Journal of Accounting Research 14(2), 246–276.

Patell standardised abnormal return; ancestor of the BMP test that factrix actually implements.

Corrado (1989)¶

Corrado, C. J. (1989). "A Nonparametric Test for Abnormal Security-price Performance in Event Studies." Journal of Financial Economics 23(2), 385–395.

Rank test on event-window abnormal returns; implemented in factrix with a direction-adjusted two-sided extension.

Corrado & Zivney (1992)¶

Corrado, C. J. & Zivney, T. L. (1992). "The Specification and Power of the Sign Test in Event Study Hypothesis Tests Using Daily Stock Returns." Journal of Financial and Quantitative Analysis 27(3), 465–478.

Sign test for event-study abnormal returns and a modified rank-test variant for two-sided / cumulative inference (re-rank within the event window); the source of the direction-adjustment idea adopted by factrix's Corrado rank-test path.

Kolari & Pynnönen (2010)¶

Kolari, J. W. & Pynnönen, S. (2010). "Event Study Testing with Cross-sectional Correlation of Abnormal Returns." Review of Financial Studies 23(11), 3996–4025.

Clustering-adjustment option on factrix's BMP-style test, scaling the BMP \(z\) by \(\sqrt{(1 - \hat r)/(1 + (N_{\mathrm{eff}}-1)\,\hat r)}\) to absorb same-date abnormal-return cross-correlation. Recommended when factrix's event-date clustering HHI diagnostic flags high concentration.

Sefcik & Thompson (1986)¶

Sefcik, S. E. & Thompson, R. (1986). "An Approach to Statistical Inference in Cross-Sectional Models with Security Abnormal Returns as Dependent Variable." Journal of Accounting Research 24(2), 316–334.

Per-event cross-sectional regression of abnormal return on a continuous event characteristic; the magnitude-weighted CAAR factrix computes when an event carries a continuous factor value is a per-event regression-slope statistic in this lineage, distinct from the equal-weighted MacKinlay-style CAAR.

Jaffe (1974)¶

Jaffe, J. F. (1974). "Special Information and Insider Trading." Journal of Business 47(3), 410–428.

Calendar-time portfolio approach to event studies — recasts event-indexed inference onto a calendar grid by forming each calendar period's portfolio of all firms with a recent event and analysing portfolio returns. Historical anchor for factrix's dense-period-grid CAAR HAC t-test, which adapts the calendar-time idea by zero-filling non-event dates on the per-event series rather than forming a calendar-period portfolio across event firms.

Mandelker (1974)¶

Mandelker, G. (1974). "Risk and Return: The Case of Merging Firms." Journal of Financial Economics 1(4), 303–335.

Independent contemporaneous calendar-time portfolio paper; cited alongside Jaffe (1974) as the joint origin of the calendar-time inference idea that factrix's sparse-panel CAAR adapts (factrix's zero-fill densification on the per-event series is a related but distinct operation from the original cross-event calendar-portfolio construction).

Fama (1998)¶

Fama, E. F. (1998). "Market Efficiency, Long-term Returns, and Behavioral Finance." Journal of Financial Economics 49(3), 283–306.

Methodological comparison of calendar-time portfolio averaging (average abnormal returns / cumulative abnormal returns) against buy-and-hold abnormal returns (BHARs), strongly recommending the calendar-time approach on the grounds that monthly returns are less susceptible to the bad-model problem and that monthly portfolio formation automatically absorbs cross-correlations of event-firm abnormal returns. The modern reference for the densification rationale underlying factrix's sparse-panel CAAR HAC path.

Multiple-testing correction and selection inference¶

Benjamini & Hochberg (1995)¶

Benjamini, Y. & Hochberg, Y. (1995). "Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing." Journal of the Royal Statistical Society: Series B 57(1), 289–300.

FDR concept and step-up procedure. factrix does not use BH directly because factor pools are typically dependent — see Benjamini-Hochberg-Yekutieli (BHY) below.

Benjamini & Yekutieli (2001)¶

Benjamini, Y. & Yekutieli, D. (2001). "The Control of the False Discovery Rate in Multiple Testing under Dependency." Annals of Statistics 29(4), 1165–1188.

BH under arbitrary dependence with the c(m) = Σ 1/i correction; provides the dependence-robust FDR adjustment that factrix's multi-factor BHY path consumes.

Simes (1986)¶

Simes, R. J. (1986). "An Improved Bonferroni Procedure for Multiple Tests of Significance." Biometrika 73(3), 751–754.

Simes' global test combining ordered p-values; used as the group representative in factrix's hierarchical FDR procedures.

Benjamini & Heller (2008)¶

Benjamini, Y. & Heller, R. (2008). "Screening for Partial Conjunction Hypotheses." Biometrics 64(4), 1215–1222.

Partial-conjunction test for "at least r of K hypotheses are true"; backs factrix's partial-conjunction p-value path.

Yekutieli (2008)¶

Yekutieli, D. (2008). "Hierarchical False Discovery Rate-Controlling Methodology." Journal of the American Statistical Association 103(481), 309–316.

Hierarchical FDR with Simes as group representative; cited as the theoretical context for the BHY + Simes composition.

Benjamini & Bogomolov (2014)¶

Benjamini, Y. & Bogomolov, M. (2014). "Selective Inference on Multiple Families of Hypotheses." Journal of the Royal Statistical Society: Series B 76(1), 297–318.

Selective-inference framework for partitioning a hypothesis set into families and controlling FDR per family. The paper's recommended form inflates the within-family level by R/m (the fraction of families flagged by an outer selection step); factrix's family-partition entry point adopts the family-partition idea but applies plain per-bucket BHY without the BB14 selection-adjusted inflation — cross-bucket selection-bias control is the caller's responsibility (e.g. via factrix's hierarchical BHY procedure).

Harvey, Liu & Zhu (2016)¶

Harvey, C. R., Liu, Y. & Zhu, H. (2016). "…and the Cross-Section of Expected Returns." Review of Financial Studies 29(1), 5–68.

Empirical case that conventional single-factor t ≥ 2.0 is too lax once the cross-section of tried factors and horizons is accounted for; HLZ argues a meaningfully higher threshold (typically t ≳ 3) under multiplicity-aware procedures. Motivation for factrix's BHY-first multi-factor discipline and its family-wise error rate (FWER)-across-horizons ∘ FDR-within-horizon stack on the horizon-shopping correction axis.

Harvey (2017)¶

Harvey, C. R. (2017). "Presidential Address: The Scientific Outlook in Financial Economics." Journal of Finance 72(4), 1399–1440.

p-hacking and replication crisis in finance; cited as motivation for factrix's pre-registered procedures and BHY-first stance.

Harvey, C. R. & Liu, Y. (2020)¶

Harvey, C. R. & Liu, Y. (2020). "False (and Missed) Discoveries in Financial Economics." Journal of Finance 75(5), 2503–2553.

Double-bootstrap procedure that jointly calibrates Type I (FDR) and Type II (miss-rate) error in asset-pricing multiple tests; the "missed-discovery" axis complements Harvey-Liu-Zhu (2016)'s Type-I-only focus by adding power-aware hurdles.

Holm (1979)¶

Holm, S. (1979). "A Simple Sequentially Rejective Multiple Test Procedure." Scandinavian Journal of Statistics 6(2), 65–70.

FWER step-down procedure that uniformly dominates Bonferroni under the same dependence assumptions; the default slice-test adjustment in factrix's multiple-testing path when callers do not supply a bootstrap distribution.

Romano & Wolf (2005)¶

Romano, J. P. & Wolf, M. (2005). "Stepwise Multiple Testing as Formalized Data Snooping." Econometrica 73(4), 1237–1282.

Bootstrap-based FWER step-down exploiting the joint dependence of test statistics; factrix's bootstrap-based FWER step-down option for the date-shared slice-test setting (e.g. universe pairwise IC).

White (2000)¶

White, H. (2000). "A Reality Check for Data Snooping." Econometrica 68(5), 1097–1126.

Bootstrap test for data-snooping bias in model-selection settings; the canonical correction factrix's greedy forward-selection path does not apply (the selection path is documented as a survivor screen, not as inference).

Hansen (2005)¶

Hansen, P. R. (2005). "A Test for Superior Predictive Ability." Journal of Business & Economic Statistics 23(4), 365–380.

Studentised refinement of the White (2000) reality check with a sample-dependent null distribution; the superior-predictive-ability (SPA) family adjacent to factrix's greedy forward-selection path.

Berk, Brown, Buja, Zhang & Zhao (2013)¶

Berk, R., Brown, L., Buja, A., Zhang, K. & Zhao, L. (2013). "Valid Post-Selection Inference." Annals of Statistics 41(2), 802–837.

PoSI inference after greedy selection; background for the known invalidity of post-selection p-values from factrix's greedy forward-selection path.

Leeb & Pötscher (2005)¶

Leeb, H. & Pötscher, B. M. (2005). "Model Selection and Inference: Facts and Fiction." Econometric Theory 21(1), 21–59.

Theoretical case against routine post-selection inference; cited alongside Berk et al. (2013).

Efron (2010)¶

Efron, B. (2010). Large-Scale Inference: Empirical Bayes Methods for Estimation, Testing, and Prediction. Cambridge University Press.

Empirical-Bayes alternative to FDR for large-scale multiple testing; reference work on local-fdr and shrinkage estimation as the empirical-Bayes counterpart to factrix's frequentist BHY stance.

Bailey & López de Prado (2014)¶

Bailey, D. H. & López de Prado, M. (2014). "The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality." Journal of Portfolio Management 40(5), 94–107.

Parallel multiple-trials correction operating on the Sharpe rather than the p-value: deflates an observed Sharpe by the expected maximum under a number-of-trials null. Related literature for the horizon-shopping multiple-trials problem on the Sharpe axis; not an implemented procedure in factrix.

Robust statistics, scale, and bootstrap¶

Huber (1964)¶

Huber, P. J. (1964). "Robust Estimation of a Location Parameter." Annals of Mathematical Statistics 35(1), 73–101.

M-estimator framework for robust location estimation under contaminated-normal models. Foundational for the broader "robustify the central tendency before it gates downstream inference" stance that factrix applies to per-date cross-sections — the MAD-as-scale lineage itself runs through Hampel (1974), not this paper.

Huber (1981)¶

Huber, P. J. (1981). Robust Statistics. Wiley.

Textbook treatment of robust scale; reference for the 1.4826 × MAD consistency factor used in factrix winsorisation.

Hampel (1974)¶

Hampel, F. R. (1974). "The Influence Curve and its Role in Robust Estimation." Journal of the American Statistical Association 69(346), 383–393.

Influence-function framework for local-robustness analysis and the canonical reference popularising the median absolute deviation as a robust scale estimator (attributing the MAD itself to Gauss). Supplies the conceptual language factrix uses for per-date robustification of scale and for breakdown-point claims on estimators such as Theil-Sen (the breakdown-point concept itself predates this paper — Hampel 1968 / 1971 — but the 1974 paper places breakdown-point reasoning and the influence function on the same conceptual map).

Rousseeuw & Croux (1993)¶

Rousseeuw, P. J. & Croux, C. (1993). "Alternatives to the Median Absolute Deviation." Journal of the American Statistical Association 88(424), 1273–1283.

\(S_n\) / \(Q_n\) estimators as higher-efficiency alternatives to MAD for robust scale (50% breakdown point, Gaussian efficiency ≈ 58% and 82% respectively vs MAD's ≈ 37%); the catalog alternative robust scale to factrix's MAD-based winsorisation.

Künsch (1989)¶

Künsch, H. R. (1989). "The Jackknife and the Bootstrap for General Stationary Observations." Annals of Statistics 17(3), 1217–1241.

Fixed-block (moving-block) bootstrap for stationary time series; underlies factrix's deterministic block-bootstrap scheme.

Politis & Romano (1994)¶

Politis, D. N. & Romano, J. P. (1994). "The Stationary Bootstrap." Journal of the American Statistical Association 89(428), 1303–1313.

Stationary block bootstrap with geometric block lengths; underlies factrix's stationary block-bootstrap scheme.

Politis & White (2004)¶

Politis, D. N. & White, H. (2004). "Automatic Block-Length Selection for the Dependent Bootstrap." Econometric Reviews 23(1), 53–70.

Data-driven block-length selector for stationary / circular bootstraps; supplies the automatic block-length choice in factrix's bootstrap path when callers do not pass one.

Sen (1968)¶

Sen, P. K. (1968). "Estimates of the Regression Coefficient Based on Kendall's Tau." Journal of the American Statistical Association 63(324), 1379–1389.

Theil-Sen median-slope estimator; the basis of factrix's breakdown-robust IC-trend slope.

Unit-root, predictive regression, and persistence¶

Dickey & Fuller (1979)¶

Dickey, D. A. & Fuller, W. A. (1979). "Distribution of the Estimators for Autoregressive Time Series with a Unit Root." Journal of the American Statistical Association 74(366), 427–431.

Dickey-Fuller unit-root test on \(H_0: \beta = 0\) in \(\Delta y_t = \alpha + \beta\, y_{t-1} + \varepsilon\); the foundational unit-root null underlying factrix's ADF persistence diagnostic. The augmented form factrix actually applies (lagged differences added to whiten serially-correlated errors) is Said-Dickey (1984), not this 1979 paper.

Said & Dickey (1984)¶

Said, S. E. & Dickey, D. A. (1984). "Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order." Biometrika 71(3), 599–607.

Approximates ARMA errors by a long autoregression and proves the Dickey-Fuller \(t\)-statistic retains its limit distribution at lag-order rate \(o(T^{1/3})\). Justifies the augmentation form that factrix's ADF persistence diagnostic relies on; concrete data-driven lag-selection rules (AIC / BIC / Ng-Perron) sit in a separate literature.

MacKinnon (1996)¶

MacKinnon, J. G. (1996). "Numerical Distribution Functions for Unit Root and Cointegration Tests." Journal of Applied Econometrics 11(6), 601–618.

Response-surface critical values for ADF; factrix interpolates linearly against the constant-only specification when converting the ADF statistic to a p-value.

Stambaugh (1999)¶

Stambaugh, R. F. (1999). "Predictive Regressions." Journal of Financial Economics 54(3), 375–421.

Finite-sample bias of ordinary least squares (OLS) \(\hat\beta\) in predictive regressions when the predictor is persistent and its innovation is correlated with the return innovation (both conditions are necessary); factrix flags the persistence channel via ADF rather than auto-correcting.

Campbell & Yogo (2006)¶

Campbell, J. Y. & Yogo, M. (2006). "Efficient Tests of Stock Return Predictability." Journal of Financial Economics 81(1), 27–60.

Bonferroni Q-test built on a DF-GLS confidence interval for the persistence parameter; a corrective-inference alternative to flag-only diagnostics for predictive regressions under near-unit-root predictors.

Phillips & Magdalinos (2009)¶

Phillips, P. C. B. & Magdalinos, T. (2009). "Econometric Inference in the Vicinity of Unity." Working paper, Singapore Management University.

Introduces IVX: mildly-integrated internal instruments yielding pivotal chi-square inference for predictive regression across integrated, near-integrated, and mildly-integrated regressors. The theoretical foundation for the Kostakis-Magdalinos-Stamatogiannis (2015) empirical implementation.

Kostakis, Magdalinos & Stamatogiannis (2015)¶

Kostakis, A., Magdalinos, T. & Stamatogiannis, M. P. (2015). "Robust Econometric Inference for Stock Return Predictability." Review of Financial Studies 28(5), 1506–1553.

Empirical IVX-Wald test for stock-return predictability robust to regressor persistence (stationary through nonstationary), supporting multivariate and long-horizon predictive specifications; the practical complement to Phillips-Magdalinos (2009) on the inference axis adjacent to factrix's ADF persistence flag.

Richardson & Stock (1989)¶

Richardson, M. & Stock, J. H. (1989). "Drawing Inferences from Statistics Based on Multiyear Asset Returns." Journal of Financial Economics 25(2), 323–348.

Alternative asymptotic theory for overlapping multiyear-return statistics under a horizon-grows-with-sample limit, where conventional asymptotics misrepresent the finite-sample distribution of long-horizon predictive coefficients. The limit-theory backstop for the HAC and sub-sampling fixes factrix applies on long-horizon paths (the sub-sampling / lag-floor remedies themselves trace to Hansen-Hodrick (1980) and the broader HAC literature, not to this paper).

Stock & Watson (1988)¶

Stock, J. H. & Watson, M. W. (1988). "Variable Trends in Economic Time Series." Journal of Economic Perspectives 2(3), 147–174.

Practitioner-oriented review of the consequences of unit roots in macroeconomic time series; cited as general background for why an ADF flag matters in factrix's IC-trend persistence path. The specific p-value threshold factrix uses for unit-root suspicion is folklore from the unit-root literature (closer to Stock 1994 Handbook of Econometrics §III) rather than a direct prescription from this paper.

Fama & French (1988)¶

Fama, E. F. & French, K. R. (1988). "Dividend Yields and Expected Stock Returns." Journal of Financial Economics 22(1), 3–25.

Canonical direct long-horizon predictive regression: summed log returns \(r_{t \to t+N} = \sum \log(P_{t+k}/P_{t+k-1})\) regressed on the dividend yield at horizons from one month to four years. Linear- additive across horizons by construction, with no compounding bias. The academic-standard alternative to arithmetic per-period normalisation; factrix's per-period normalisation choice is a scale-comparability convention, not an empirical claim derived from this paper.

Boudoukh, Richardson & Whitelaw (2008)¶

Boudoukh, J., Richardson, M. & Whitelaw, R. F. (2008). "The Myth of Long-Horizon Predictability." Review of Financial Studies 21(4), 1577–1605.

Under the null and a persistent regressor (most factor signals), OLS slope estimators across horizons are highly correlated — approaching unity between adjacent horizons at dividend-yield-like persistence — and R² is roughly proportional to horizon. Across-horizon test statistics are not independent and BHY's positive regression dependence on a subset (PRDS) assumption fails, so factrix uses an FWER (independence-free) inner step before BHY in its multi-factor BHY path — the FWER prescription is factrix's response to BRW's correlation result, not BRW's own recommendation. Also motivates treating per-period scaling as separate from inference in factrix's forward-return path: the across-horizon dependence BRW documents is not addressed by any normalisation choice.

Factor zoo, replication, and out-of-sample (OOS) decay¶

McLean & Pontiff (2016)¶

McLean, R. D. & Pontiff, J. (2016). "Does Academic Research Destroy Stock Return Predictability?" Journal of Finance 71(1), 5–32.

Empirical ~32% post-publication decay in factor returns; the canonical OOS-decay benchmark underlying factrix's multi-split OOS-decay procedure.

Hou, Xue & Zhang (2020)¶

Hou, K., Xue, C. & Zhang, L. (2020). "Replicating Anomalies." Review of Financial Studies 33(5), 2019–2133.

Large-scale replication of published anomalies under NYSE-breakpoint, value-weighted testing that jointly mitigates microcap influence — ~65% of 452 anomalies fail \(|t| \geq 1.96\) once both microcap mitigations are applied. The headline reason factrix prefers value-weighted spreads in capacity-constrained settings.

Chen & Zimmermann (2022)¶

Chen, A. Y. & Zimmermann, T. (2022). "Open Source Cross-Sectional Asset Pricing." Critical Finance Review 11(2), 207–264.

Open-source reproduction of 300+ cross-sectional anomalies with public data and code; the empirical reproducibility anchor for factrix's downstream slice-conditional IC analyses (regime, universe, or other slice-axis stratifications layered on top of a reproducible characteristic set).

López de Prado (2018)¶

López de Prado, M. (2018). Advances in Financial Machine Learning. Wiley.

CPCV (Combinatorial Purged CV) and broader ML-aware backtesting discipline; the robust train/test alternative to factrix's multi-split OOS-decay path.

Green, Hand & Zhang (2017)¶

Green, J., Hand, J. R. M. & Zhang, X. F. (2017). "The Characteristics that Provide Independent Information about Average U.S. Monthly Stock Returns." Review of Financial Studies 30(12), 4389–4436.

Simultaneous Fama-MacBeth regression of ~90 firm characteristics on cross-sectional returns, identifying the small subset that retains independent explanatory power and documenting the post-2003 collapse of the broader characteristic zoo. Empirical anchor for taking characteristic redundancy seriously in multi-factor screening (not for univariate IC ranking, which is the simpler — and weaker — methodology factrix exposes alongside the multi-factor BHY path).

Jensen, Kelly & Pedersen (2023)¶

Jensen, T. I., Kelly, B. & Pedersen, L. H. (2023). "Is There a Replication Crisis in Finance?" Journal of Finance 78(5), 2465–2518.

Bayesian hierarchical re-evaluation of the factor zoo; concludes most published anomalies replicate after appropriate priors. Cited in design notes as the "why not Bayesian" comparison.

Lou & Polk (2022)¶

Lou, D. & Polk, C. (2022). "Comomentum: Inferring Arbitrage Activity from Return Correlations." Review of Financial Studies 35(7), 3272–3302.

Comomentum measures crowding from cross-asset return correlations within momentum winners and losers. A suggestive crowding explanation for downward-sloping IC over time in factrix's IC-trend interpretation; the paper's direct subject is return comomentum, not IC slope — McLean-Pontiff 2016 is the cleaner cite for post-publication IC decay.

Factor spanning, selection, and active-management heuristics¶

Barillas & Shanken (2017)¶

Barillas, F. & Shanken, J. (2017). "Which Alpha?" Review of Financial Studies 30(4), 1316–1338.

Spanning-test framework for traded-factor model comparison: model comparison reduces to whether each model prices the other model's factors (left-hand-side = competing factors, not test assets), and the result applies to nested and non-nested comparisons alike. The methodology behind factrix's spanning-alpha procedure.

Barillas & Shanken (2018)¶

Barillas, F. & Shanken, J. (2018). "Comparing Asset Pricing Models." Journal of Finance 73(2), 715–754.

Bayesian model-comparison alternative; cited in design notes as the "why not Bayesian" comparison for spanning tests.

Feng, Giglio & Xiu (2020)¶

Feng, G., Giglio, S. & Xiu, D. (2020). "Taming the Factor Zoo: A Test of New Factors." Journal of Finance 75(3), 1327–1370.

Two-pass model-selection-corrected stochastic discount factor (SDF) estimator with double-selection LASSO for testing whether a candidate factor adds incremental pricing power; the principled selection-aware counterpart to greedy stepwise factor spanning.

Gibbons, Ross & Shanken (1989)¶

Gibbons, M. R., Ross, S. A. & Shanken, J. (1989). "A Test of the Efficiency of a Given Portfolio." Econometrica 57(5), 1121–1152.

GRS test for joint α = 0 across portfolios; the parametric ancestor of factrix's spanning toolkit.

Kozak, Nagel & Santosh (2020)¶

Kozak, S., Nagel, S. & Santosh, S. (2020). "Shrinking the Cross Section." Journal of Financial Economics 135(2), 271–292.

Bayesian shrinkage on the SDF coefficients; cited in design notes as the "why not Bayesian" comparison for factor selection.

Patton & Timmermann (2010)¶

Patton, A. J. & Timmermann, A. (2010). "Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM, and Portfolio Sorts." Journal of Financial Economics 98(3), 605–625.

Bootstrap-based formal tests for monotonic relations across sorted-portfolio expected returns; the inference-grade benchmark for monotonicity diagnostics on portfolio sorts.

Novy-Marx & Velikov (2016)¶

Novy-Marx, R. & Velikov, M. (2016). "A Taxonomy of Anomalies and Their Trading Costs." Review of Financial Studies 29(1), 104–147.

Turnover, generalised buy/hold spreads, and breakeven-cost analysis of anomaly portfolios; the lineage for turnover-aware and breakeven-cost diagnostics.

DeMiguel, Martin-Utrera, Nogales & Uppal (2020)¶

DeMiguel, V., Martin-Utrera, A., Nogales, F. J. & Uppal, R. (2020). "A Transaction-cost Perspective on the Multitude of Firm Characteristics." Review of Financial Studies 33(5), 2180–2222.

Transaction-cost-aware joint selection across firm characteristics; the structural reason gross-spread diagnostics require a cost-deduction counterpart for capacity-aware research.

DeMiguel, Garlappi & Uppal (2009)¶

DeMiguel, V., Garlappi, L. & Uppal, R. (2009). "Optimal Versus Naive Diversification: How Inefficient is the 1/N Portfolio Strategy?" Review of Financial Studies 22(5), 1915–1953.

Equal-weight benchmark; cited in design notes as the "why no optimisation" comparison.

Asness, Moskowitz & Pedersen (2013)¶

Asness, C. S., Moskowitz, T. J. & Pedersen, L. H. (2013). "Value and Momentum Everywhere." Journal of Finance 68(3), 929–985.

Cross-asset, cross-market documentation of value and momentum premia with common factor structure across eight markets and asset classes; the canonical reference for cross-market factor-evaluation patterns.

Ambachtsheer (1977)¶

Ambachtsheer, K. P. (1977). "Where Are the Customers' Alphas?" Journal of Portfolio Management 4(1), 52–56.

Early operational use of IC-based alpha attribution in pension-fund performance discussion; the appraisal-ratio ancestor of the formal \(\mathrm{IR} \approx \mathrm{IC} \times \sqrt{\mathrm{breadth}}\) decomposition is Treynor & Black (1973), and the breadth identity itself is canonically derived in Grinold 1989.

Methodology critique and composite-score design¶

Goodhart (1984)¶

Goodhart, C. A. E. (1984). "Problems of Monetary Management: The UK Experience." In Monetary Theory and Practice. Macmillan.

Original monetary-policy statement of Goodhart's Law: any observed statistical regularity tends to collapse once it is pressed into service as a control target. (The familiar paraphrase "when a measure becomes a target, it ceases to be a good measure" is Strathern's 1997 reformulation, not Goodhart's own wording.) Cited as the structural argument against composite factor scores.

Cochrane (2005)¶

Cochrane, J. H. (2005). Asset Pricing (Revised ed.). Princeton University Press.

Textbook treatment of the SDF framework underlying factrix's spanning and FM tests.

Cochrane (2011)¶

Cochrane, J. H. (2011). "Presidential Address: Discount Rates." Journal of Finance 66(4), 1047–1108.

The "factor zoo" critique that motivates BHY-first multi-factor discipline.

Herfindahl (1950)¶

Herfindahl, O. C. (1950). Concentration in the U.S. Steel Industry. PhD dissertation, Columbia University.

Independent formulation (squared-share form) of the index used by factrix's concentration / clustering diagnostics; paired with Hirschman (1945) as the full HHI lineage. The squared form that modern HHI follows comes from this paper.

Hirschman (1945)¶

Hirschman, A. O. (1945). National Power and the Structure of Foreign Trade. University of California Press.

Earlier (1945) priority for the foreign-trade concentration index, using the square-root form of the squared-share sum; paired with Herfindahl (1950) (whose squared form modern HHI adopts) as the full HHI lineage.

Jacquier, Kane & Marcus (2003)¶

Jacquier, E., Kane, A. & Marcus, A. J. (2003). "Geometric or Arithmetic Mean: A Reconsideration." Financial Analysts Journal 59(6), 46–53.

Compounding at the arithmetic mean is an upward-biased estimator of cumulative wealth; the geometric mean is downward-biased; the unbiased estimator is a horizon-weighted blend of the two with weights depending on the forecast-horizon / sample-length ratio. The compounding-bias caveat underlying factrix's per-period forward-return normalisation.