Classification of Extremal Dependence in Financial Markets via Bootstrap Inference

Qian Hui; Sidney I. Resnick; Tiandong Wang

REVIEW 4 major objections 5 minor 12 references

Classification of Extremal Dependence in Financial Markets via Bootstrap Inference

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A bootstrap test classifies every pair of 66 stocks into four tail-dependence types and finds U.S. sectors cluster in isolation while Chinese sectors are broadly interconnected.

desk verdict A clean, honest application of a self-developed bootstrap classifier to U.S. and Chinese equity pairs; the empirical map is new and worth a look, but the iid assumption after every-other-day sampling is the main thing to pressure-test. read the letter →

arxiv 2506.04656 v1 pith:KA3NVJKY submitted 2025-06-05 math.ST q-fin.STstat.TH

Qian Hui , Sidney I. Resnick , Tiandong Wang This is my paper

classification math.STq-fin.STstat.TH MSC 62G3262G0962P05

keywords extremaldependenceasymptoticangularmeasurebootstrapinferencemultivariateregularvariationheavy-taileddatafinancialreturnsU.S.andChinesestockmarkets

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

This paper applies a bootstrap-based hypothesis testing procedure to the absolute log returns of 66 stocks (three from each of 11 sectors in the U.S. S&P 500 and Chinese A-shares) to classify every stock pair into one of four tail-dependence types: asymptotic independence, weak dependence, strong dependence, or full dependence. The central empirical finding is that U.S. stocks form more isolated clusters of dependent assets, while Chinese sectors are more broadly interconnected, and that cross-market extreme linkages are strongest in materials, consumer staples, and consumer discretionary. A sympathetic reader would care because this offers a largely automated, threshold-robust way to read the extreme-risk network of a large set of assets, replacing eyeballing angular histograms with a formal classification.

What carries the argument

The central object is the angular measure $S$ on $[0,1]$ arising from the $L_1$ polar transform of a bivariate regularly varying vector, whose support encodes the four dependence types: $\{0,1\}$ for asymptotic independence, a proper subinterval $[a,b]$ for strong dependence, a single point for full dependence, and all of $[0,1]$ for weak dependence. The engine is a pair of test statistics: $D_n$, built from the distance of extreme observations to a cone $C_{a,b}$, and $T_n$, a radial-log weighted average of angles, together with a bootstrap step that resamples $m = o(n)$ observations so that plugging in the Hill estimator does not make the asymptotic distributions degenerate. The bootstrap p-values drive the sequential four-way classification.

What would settle it

Recompute the four-way classifications on the same 66 stocks using daily (not every-other-day) absolute returns, or using a stationary block bootstrap that preserves serial dependence; if the U.S.-China contrast or the sector-level clusters change substantially, the iid assumption is not negligible.

Watch

Extended reading notes

Core claim

The paper's core claim is that the support of the angular measure of multivariate regularly varying tails carries enough information to separate four asymptotic dependence regimes, and that a bootstrap version of the D_n and T_n tests from Wang and Resnick (2025a) can make that separation operational on 66 real return series. On the data, the classification shows no asymptotic independence among the selected U.S. stocks, Chinese stocks, or U.S.-China pairs; instead, U.S. sectors display more structured, segmented clusters of full and strong dependence centered on financials and technology, while Chinese sectors display heavy full dependence across consumer staples and consumer discretionary, consistent with a more interconnected economy. The strongest cross-market linkages appear in materials, consumer staples, and consumer discretionary, which the paper attributes to trade ties and global supply chains.

Load-bearing premise

The whole classification stands on the assumption that the every-other-day absolute log returns are effectively an iid sample; if volatility clustering still lingers at that horizon, the bootstrap p-values and the U.S.-China difference could be miscalibrated.

Editorial extensions

If this is right

The same bootstrap procedure can classify thousands of stock pairs automatically, with only a formulaic threshold choice, so sector-level tail dependence maps are reproducible.
Within the U.S. market, financials and technology are central to the extreme-dependence network, while healthcare, consumer staples, and utilities are more peripheral.
Within China, consumer staples and consumer discretionary are heavily full-dependent on other sectors, while utilities are comparatively isolated.
Across the two economies, extreme shocks in materials, consumer staples, and consumer discretionary are likely to propagate between the U.S. and China, while energy, real estate, technology, and regulated sectors show little cross-market tail dependence.

Reading between the lines

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

A direct extension would be to run the same classification on block-bootstrapped or temporally clustered samples to test how much of the U.S.-China contrast survives serial dependence in volatility.
The classification could be projected onto a network of assets, with full and strong dependence as edges, turning the sector summaries into formal centrality and community-structure measures.
The every-other-day sampling choice implies a testable prediction: classifications should be stable when moving from daily to weekly absolute returns if serial dependence is truly mitigated; instability would signal that the iid assumption is doing real work.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The new content here is the empirical classification: 66 U.S. and Chinese stocks, 11 sectors, all pairs run through the Wang–Resnick bootstrap procedure, and the sector-level comparison (U.S. more isolated, China more interconnected, cross-market links in materials and consumer sectors). That map is not in the earlier papers, and it is the kind of reproducible empirical output that makes the paper useful. The authors are transparent about the tuning choices, repeat the procedure 50 times per pair, and they flag that the threshold selection is automated because individual Hill plots were impractical. Credit where due: the method is theirs, the data are publicly available in principle, and the presentation is clear.

The soft spots are real but not fatal. The biggest one is the same as your stress-test: Section 3.1 justifies every-other-day sampling by citing Cont, Drost–Nijman, and Lo–MacKinlay, but the bootstrap theory in Section 2.1 is iid. They never check whether residual serial dependence survives in the 66 absolute-return series, and they do not run a Ljung–Box or a block-bootstrap comparison. Since the two markets can have different persistence profiles, the U.S.–China contrast could partly reflect differential dependence rather than pure tail support. The paper itself concedes this is not tested; that is an honest omission, but it is still the load-bearing assumption. Second, the null in Step 4 uses the estimated interval [a_hat, b_hat] from the same data, and the bootstrap critical values rely on plug-in estimates. Wang and Resnick (2025b) reportedly handles the theory, but that manuscript is not public, so a referee cannot independently check the calibration. Third, the tuning parameters (lambda=4, m=ceil(6n/k(n)), k(m)=ceil(2m^0.4), the 0.85 interval cutoff) are ad hoc. They say these align with Wang–Resnick (2025a), but no sensitivity analysis is reported. These are fixable with a few robustness checks: re-run with alternative lambda and block bootstrap, report serial-correlation diagnostics on the sampled series, and provide a supplementary table of classifications under two or three threshold rules. None of this looks like misconduct; it is standard empirical methodology that needs more validation.

Who is this for? Researchers in extremal dependence and financial econometrics who want a worked example of the bootstrap classification approach on real data. It is not a theory paper, but it demonstrates the method's scalability. A serious referee could push on the iid assumption and the lack of sensitivity analysis, and the paper would be stronger for it. I would accept it for peer review, conditional on those checks. I would not cite the empirical U.S.–China contrast as established until the robustness work is done.

Referee Report

4 major / 5 minor

Summary. The manuscript applies the bootstrap-based classification procedure of Wang and Resnick (2025a, 2025b) to bivariate pairs of absolute log returns of 33 U.S. S&P 500 and 33 Chinese A-share stocks over 2016-2022, with every-other-day sampling, classifying each pair into asymptotic independence, weak dependence, strong dependence, or full dependence. The authors report that U.S. sectors show more isolated clustering of dependent assets, Chinese sectors show a more interconnected extremal dependence pattern, and the strongest cross-market linkages are in materials, consumer staples, and consumer discretionary. The paper is primarily an empirical application; the theoretical framework is inherited from earlier work.

Significance. If the classifications are valid, the paper demonstrates a scalable bootstrap-based approach to extremal dependence classification and provides a substantive stylized fact about tail dependence in the U.S. and Chinese equity markets. The manuscript is transparent about its many tuning inputs and repeats the classification 50 times to assess stability, which is commendable for an automated large-scale study. However, the central empirical claims currently rest on several unvalidated assumptions and hand-chosen parameters: the iid bootstrap theory is applied to time series without a reported serial-dependence diagnostic; the first null hypothesis is defined using an interval estimated from the same data; and the finite-sample behavior of the bootstrap statistics is not calibrated. These issues affect the size of the tests and therefore the classification frequencies, so the reported U.S.-China contrast is not yet established.

major comments (4)

[Section 2.1 and Section 3.1] The bootstrap theory in Section 2.1 starts with 'Consider iid data' in Eq. (1), and the resampling in Steps 2-3 of Algorithm 1 is the ordinary iid multinomial bootstrap. Section 3.1 justifies every-other-day sampling only by citing Cont (2001), Drost and Nijman (1993), and Lo and MacKinlay (1988) to argue that coarser sampling weakens serial dependence, but no diagnostic is reported for the 66 absolute-return series actually used. Since GARCH temporal aggregation reduces rather than eliminates volatility persistence and absolute returns routinely exhibit long-range dependence, the effective size of the 5% and chi-square rejection rules in Steps 4-6 is not controlled. This concern is load-bearing because the reported U.S.-China contrast could be an artifact of differential residual dependence. Please report serial-correlation diagnostics (e.g., Ljung-Box on absolute returns at the every-other-day horizon) and repeat the classification with a dependence-preserving resampling scheme such as a moving-block bootstrap.
[Algorithm 1, Step 2 and Step 4] The null hypothesis H0(1): S([a_hat,b_hat]) = 1 is defined after (a_hat,b_hat) have been estimated from the same data by minimizing (b-a) + lambda*sqrt(k(n))*|D_n - 1/alpha_hat|. Because the interval is chosen to bring D_n close to 1/alpha_hat, the first test is biased toward accepting strong dependence, and the bootstrap critical values condition on these plug-in estimates without accounting for their variability. The manuscript does not provide a calibration simulation under known dependence types, so the classification frequencies in Figures 2-5 may overstate strong/full dependence. Please assess this selection effect, for example by sample-splitting or by simulating the full procedure under models satisfying Eq. (1).
[Section 3.1, parameter choices] The paper chooses m = ceil(6n/k(n)) and k(m) = ceil(2m^0.4), which with n = 822 and k(n) near 80-120 gives m near 40-60 and k(m) near 9-11. The asymptotic justification for the bootstrap statistics in Steps 4-6 relies on k(m) growing, and using such small bootstrap tail samples in a fully automated procedure requires finite-sample validation. In addition, the threshold 80+min{40,(k*(n)-80)+}, lambda = 4, B = 200, the 0.85 interval-length rule, and the 50 repetitions are all hand-chosen, and no sensitivity analysis is presented. Since the main conclusions are qualitative comparisons between two markets, a grid over these inputs should be shown to leave the sector-level pattern unchanged.
[Section 3.2] The classification is applied to 33 choose 2 within each market plus 33 x 33 cross pairs, roughly 2,145 pairs, and each pair is subjected to several 5% tests. The paper does not control the familywise error or false discovery rate across these pairs, and the phrase 'we follow Bonferroni's method' at a per-test significance level of 0.025 does not address multiplicity. Moreover, the results are presented only as color-coded matrices and no numerical table of the averaged classification vectors or p-values is provided. Please include multiplicity-corrected summaries and a data/code availability statement so the reader can verify the visual claims.

minor comments (5)

[Algorithm 1, Step 5] The text says 'using T_i,boot_m, i=1,...,m' but the loop is over B bootstrap samples; this should be i=1,...,B.
[Section 3.1] The 0.85 interval-length rule is introduced without any statistical rationale; given its direct effect on which branch of Algorithm 1 is followed, at least a brief justification or sensitivity check is needed.
[Table 1 and Appendix A] Chinese stocks are listed only by company name in Table 1; provide tickers or IDs to make the data selection reproducible. Also, many names in Appendix A have spelling artifacts (e.g., 'W anda', 'MET A', 'IFL YTEK').
[References] The bootstrap justification relies on Wang and Resnick (2025b), cited as 'Manuscript in preparation'; this is not publicly available, making the theoretical basis of the procedure difficult to verify.
[Section 3.2] The narrative interpretation of the color maps is subjective (e.g., 'more gray' vs 'less gray'); add quantitative summaries such as frequencies of each classification averaged across the 50 repetitions.

Circularity Check

2 steps flagged · score 5.0 of 10

The strong-dependence test's null interval is fitted from the same data, and bootstrap validity rests on an unpublished self-citation.

self definitional [Section 2.2, Steps 2 and 4 (estimation of (a_hat,b_hat) and test H0^(1))]
"Using the original sample, estimate the parameter vector ( α, a, b). For α use the Hill estimator and (ˆa, ˆb) are consistently estimated by (ˆa, ˆb) := arg min_{0<a≤b≤1} n (b − a) + λ p k(n) |Dn − 1/ˆα| o ... Step 4. Start by testing the existence of strong dependence: H (1) 0 : S([ˆa, ˆb]) = 1 vs H (1) a : S([ˆa, ˆb]) < 1, using the simple statistics D i,boot m ... reject if |D i,boot m − 1/ˆα| > 1.96 1/ˆαp k(m)"

The null set [a_hat,b_hat] is not pre-specified; it is the minimizer of (b−a)+λ√k |D_n(a,b)−1/α_hat|. Since D_n(a,b) converges to 1/α precisely when S([a,b])=1 (no angular mass outside the fitted cone), the estimator is an automated search for an interval that makes the sample version of H0 true. The same fitted interval is then plugged into the bootstrap statistic and compared to the same 1/α_hat threshold to accept strong dependence. Thus the strong-dependence classification is to a significant degree the output of the fit, not an independent test of a fixed null hypothesis.
self citation load bearing [Section 2.1, after Eq. (5)]
"Theoretical justification of the bootstrap method is provided in Wang and Resnick (2025b)."

Every empirical classification in Steps 1-6 depends on the bootstrap null distributions, but the paper supplies no proof or validation of its own. The cited justification is an unpublished 'Manuscript in preparation' by two of the present authors (Wang and Resnick 2025b). The bootstrap's validity is therefore carried by a self-citation whose content is not independently verifiable in this paper, so the 'procedure reveals' claims lean on an unverified citation chain rather than on a derivation reproduced here.

full rationale

The paper is an application of a published bootstrap testing framework, and most of the data analysis (pairwise classifications, sector summaries) is grounded in empirical data rather than in a single fitted parameter. I find no global 'everything is defined in terms of everything else' circularity. However, two load-bearing moves are circular in a narrower sense. First, the test for strong dependence defines H0^(1) as S([a_hat,b_hat])=1 using an interval that is estimated from the same data by minimizing |D_n(a,b)-1/α_hat|; because D_n→1/α is exactly the null condition, the interval is fitted to satisfy the null and the subsequent bootstrap test evaluates that same fitted null. This is a data-dependent null and biases the strong-dependence classification toward acceptance. Second, the validity of the bootstrap critical values used for every p-value is delegated to Wang and Resnick (2025b), an unpublished manuscript by two of the present authors, so the central empirical claims rest on an unverified self-citation. These issues do not make the U.S.-China contrast entirely vacuous: the pairwise data, the weak-dependence/independence leg of the algorithm, and the cross-market comparisons still supply independent information. But the circularity burden is moderate, so the overall score is 5.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper contributes no new entities. Its central claim rests on the iid assumption, the regular variation model, the unpublished bootstrap justification, and several hand-chosen tuning parameters (lambda, threshold formula, bootstrap sizes, interval-length cutoff). These choices are disclosed but not derived or stress-tested, so the reader is asked to take a large upstream package on faith.

free parameters (5)

Tuning parameter lambda = 4
Chosen by hand in Step 2 of Section 2.2 for the estimator of (a,b). It controls the penalty on interval length versus distance to the cone and directly affects which interval is used in the first bootstrap test.
Modified minimum-distance threshold = 80 + min{40,(k*(n)-80)+}
Hand-formula applied to the data-driven k*(n) from the minimum distance method in Section 3.1. This determines the number of extremes used for Hill estimation and hence all test inputs; no sensitivity analysis is given.
Bootstrap sample size multipliers = m = ceil(6n/k(n)), k(m) = ceil(2m^0.4), B = 200
Chosen in Section 3.1 following Wang and Resnick (2025a). These control the bootstrap distribution and the chi-square cutoff; no justification for these specific values is provided.
Interval-length adjustment cutoff = 0.85
If b_hat - a_hat >= 0.85, the paper skips the strong-dependence test and directly tests weak versus independence in Section 3.1. This changes the classification path for wide-support pairs and is justified only by experience.
Per-test significance level = 0.025 with Bonferroni
Section 3.1 states the significance level is set at 0.025 with Bonferroni correction, but the number of tests being corrected is not specified. Ambiguity in the multiple-testing correction affects the reported classifications.

assumptions (4)

domain assumption The every-other-day absolute log returns are approximately iid, as required by Equation (1).
Section 3.1 relies on lower-frequency sampling to weaken serial dependence but does not test residual dependence before applying the iid-based bootstrap theory.
domain assumption Each stock's absolute log return is heavy-tailed and the bivariate pairs satisfy multivariate regular variation with a common tail index after a power transformation.
The setup in Equations (1)-(2) assumes multivariate regular variation; the authors apply a power transformation to make the common tail index the average of the two Hill estimates in Section 3.1, and this transformation is asserted, not derived.
domain assumption The bootstrap procedure of Wang and Resnick (2025b) is valid for the sample sizes and parameter choices used here.
The paper relies on Wang and Resnick (2025b), cited as 'Manuscript in preparation', for the bootstrap justification. This result is not available to readers to verify.
domain assumption The estimated interval [a_hat,b_hat] used in the null hypothesis of the first test provides a valid data-dependent null for the bootstrap.
Step 2 estimates (a_hat,b_hat) from the same data and Step 4 then tests whether the support is contained in this estimated interval; the validity of testing a data-dependent null is not discussed in the paper.

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Pith. "Pith review of Classification of Extremal Dependence in Financial Markets via Bootstrap Inference." pith.science (2026). https://pith.science/paper/KA3NVJKY

@misc{pith2026250604656,
  author       = {Pith},
  title        = {Pith review of: Classification of Extremal Dependence in Financial Markets via Bootstrap Inference},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KA3NVJKY}},
  note         = {Machine review of arXiv:2506.04656}
}

read the original abstract

Accurately identifying the extremal dependence structure in multivariate heavy-tailed data is a fundamental yet challenging task, particularly in financial applications. Following a recently proposed bootstrap-based testing procedure, we apply the methodology to absolute log returns of U.S. S&P 500 and Chinese A-share stocks over a time period well before the U.S. election in 2024. The procedure reveals more isolated clustering of dependent assets in the U.S. economy compared with China which exhibits different characteristics and a more interconnected pattern of extremal dependence. Cross-market analysis identifies strong extremal linkages in sectors such as materials, consumer staples and consumer discretionary, highlighting the effectiveness of the testing procedure for large-scale empirical applications.

Figures

Figures reproduced from arXiv: 2506.04656 by the authors.

**Figure 2.** Extremal dependence structures; blue, yellow and gray squares represent asymptotic full, [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗

**Figure 3.** Extremal dependence of sectors within the U.S. market emphasizing utilities, financials [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: Extremal dependence of sectors within the Chinese market emphasizing utilities, con [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

**Figure 5.** Figure 5: Extremal dependence structures between the U.S. and Chinese stock markets. Blue, [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]

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Reference graph

Works this paper leans on

12 extracted references · 12 canonical work pages

[1]

Classification of Extremal Dependence in Financial Markets via Bootstrap Inference Qian Hui1, Sidney I. Resnick 2, and Tiandong Wang ∗1,3 1Shanghai Center for Mathematical Sciences, Fudan University 2School of Operations Research and Information Engineering, Cornell University 3Shanghai Academy of Artificial Intelligence for Science August 29, 2025 In fon...

work page 2025
[4]

2 Preliminaries {sec:prelim} 2.1 Dependence Structure Consider iid data from the common distribution of a random vector Z := ( X, Y) ∈ R2 + with P[Z ∈ ·] satisfying tP[Z/b(t) ∈ ·] → η(·), (t → ∞), (1) {e:regVar} {e:regVar} for a measure η(·) on R2 + \ {0} and some regularly varying scaling function b(t) → ∞. Apply the L1 polar transformation: R = X + Y, Θ...

work page 2014
[5]

(Other approaches to handle asymptotic independence can be found in (Lehtomaa and Resnick 2020; Resnick 2024).) Assuming an iid sample Z1,

For instance, assume g(θ) =    1 − 2θ, if 0 ≤ θ <1 2 , 3 − 2θ, if 1 2 ≤ θ ≤ 1, then an asymptotically independent heavy tailed distribution is transformed to a distribution with fully dependent tail. (Other approaches to handle asymptotic independence can be found in (Lehtomaa and Resnick 2020; Resnick 2024).) Assuming an iid sample Z1, . . . ,Zn wit...

work page 2020
[6]

Note that the asymptotic variance of Tn varies by case, and is smallest under full dependence, which helps in classifying these cases

To distinguish the asymptotic dependence structure, Wang and Resnick (2025a) propose two test statistics Dn := 1 k(n) k(n)X i=1 1 + d Z∗ i , Ca,b R(k(n)) ! log R(i) R(k(n)) , T n := Pk(n) i=1 Θ∗ i log R(i) R(k(n)) Pk(n) i=1 Θ∗ i , (5) {e:teststats} {e:teststats} and under mild conditions, Wang and Resnick (2025a) have proved that two test statistics Dn = ...

work page 2025
[7]

The bootstrap sample size is taken as m = m(n)= o(n) following Athreya (1987); Gin´ e and Zinn (1989); Feigin and Resnick (1997); Resnick (2007)

For a given sample size n, choose k = k(n)→ ∞such that k(n)/n → 0, and use the k(n) largest observations for estimates. The bootstrap sample size is taken as m = m(n)= o(n) following Athreya (1987); Gin´ e and Zinn (1989); Feigin and Resnick (1997); Resnick (2007). Also, drawB bootstrap samples of size m from the original sample. These samples are taken i...

work page 1987
[8]

{alg:test} Require: Estimate α, a and b from the original sample, denoted as ˆα, ˆa and ˆb

Algorithm 1 Testing procedure. {alg:test} Require: Estimate α, a and b from the original sample, denoted as ˆα, ˆa and ˆb. 1: Test H (1) 0 : S([ˆa, ˆb]) = 1 vs H (1) a : S([ˆa, ˆb]) < 1, using Dboot m . 2: if Accept H (1) 0 then 3: Test H (2) 0 : supp(S) is a single point vs H (2) a : supp(S) is not a single point using T boot m . 4: if Accept H (2) 0 the...

work page 2016
[10]

Presumably this reflects Chinese manufacturing expertise of consumer 12 goods

we sees heavy doses of blue for the sectors consumer staples and consumer discretionary indicating these sectors are heavily dependent on other economic sectors. Presumably this reflects Chinese manufacturing expertise of consumer 12 goods. Despite these differences between the U.S. and China, both markets show some similarities in the utilities sector, w...

work page 1987
[223]

Das, B. and S. Resnick (2017). Hidden regular variation under full and strong asymptotic depen- dence. Extremes 20 (4), 873–904. 15 Drees, H., A. Janßen, and Resnick, S.I., Wang, T. (2020). On a minimum distance procedure for threshold selection in tail analysis. Siam J. Math. Data Sci. 2 (1), 75–102. Drost, F. and T. Nijman (1993). Temporal aggregation o...

work page 2017

Show all 12 references

[277]

Resnick, and J

Lindskog, F., S. Resnick, and J. Roy (2014). Regularly varying measures on metric spaces: Hidden regular variation and hidden jumps. Probab. Surv. 11, 270–314. Lo, A. W. and A. C. MacKinlay (1988). Stock market prices do not follow random walks: Evidence from a simple specific...

2014
[2020]

Despite knowing the minimum distance method can have drawbacks (Drees et al

to obtain k∗(n). Despite knowing the minimum distance method can have drawbacks (Drees et al. 2020), the large number datasets meant it was impractical to individually analyze each of them by examining Hill plots to check how sensible the minimum distance tail estimates seemed...

2020
[2022]

election

This time period is prior to the 2024 U.S. election. The 66 stocks selected for comparison represent 11 sectors from both the U.S. and China, with three stocks per sector. Table 1 lists the sectors and the representative stocks chosen in each sector, and in Appendix A we provi...

2001
[2024]

economy compared with China which exhibits different characteristics and a more interconnected pattern of extremal dependence

The procedure reveals more isolated clustering of dependent assets in the U.S. economy compared with China which exhibits different characteristics and a more interconnected pattern of extremal dependence. Cross-market analysis identifies strong extremal linkages in sectors su...

2017 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.

[1] [1]

Classification of Extremal Dependence in Financial Markets via Bootstrap Inference Qian Hui1, Sidney I. Resnick 2, and Tiandong Wang ∗1,3 1Shanghai Center for Mathematical Sciences, Fudan University 2School of Operations Research and Information Engineering, Cornell University 3Shanghai Academy of Artificial Intelligence for Science August 29, 2025 In fon...

work page 2025

[2] [4]

2 Preliminaries {sec:prelim} 2.1 Dependence Structure Consider iid data from the common distribution of a random vector Z := ( X, Y) ∈ R2 + with P[Z ∈ ·] satisfying tP[Z/b(t) ∈ ·] → η(·), (t → ∞), (1) {e:regVar} {e:regVar} for a measure η(·) on R2 + \ {0} and some regularly varying scaling function b(t) → ∞. Apply the L1 polar transformation: R = X + Y, Θ...

work page 2014

[3] [5]

(Other approaches to handle asymptotic independence can be found in (Lehtomaa and Resnick 2020; Resnick 2024).) Assuming an iid sample Z1,

For instance, assume g(θ) =    1 − 2θ, if 0 ≤ θ <1 2 , 3 − 2θ, if 1 2 ≤ θ ≤ 1, then an asymptotically independent heavy tailed distribution is transformed to a distribution with fully dependent tail. (Other approaches to handle asymptotic independence can be found in (Lehtomaa and Resnick 2020; Resnick 2024).) Assuming an iid sample Z1, . . . ,Zn wit...

work page 2020

[4] [6]

Note that the asymptotic variance of Tn varies by case, and is smallest under full dependence, which helps in classifying these cases

To distinguish the asymptotic dependence structure, Wang and Resnick (2025a) propose two test statistics Dn := 1 k(n) k(n)X i=1 1 + d Z∗ i , Ca,b R(k(n)) ! log R(i) R(k(n)) , T n := Pk(n) i=1 Θ∗ i log R(i) R(k(n)) Pk(n) i=1 Θ∗ i , (5) {e:teststats} {e:teststats} and under mild conditions, Wang and Resnick (2025a) have proved that two test statistics Dn = ...

work page 2025

[5] [7]

The bootstrap sample size is taken as m = m(n)= o(n) following Athreya (1987); Gin´ e and Zinn (1989); Feigin and Resnick (1997); Resnick (2007)

For a given sample size n, choose k = k(n)→ ∞such that k(n)/n → 0, and use the k(n) largest observations for estimates. The bootstrap sample size is taken as m = m(n)= o(n) following Athreya (1987); Gin´ e and Zinn (1989); Feigin and Resnick (1997); Resnick (2007). Also, drawB bootstrap samples of size m from the original sample. These samples are taken i...

work page 1987

[6] [8]

{alg:test} Require: Estimate α, a and b from the original sample, denoted as ˆα, ˆa and ˆb

Algorithm 1 Testing procedure. {alg:test} Require: Estimate α, a and b from the original sample, denoted as ˆα, ˆa and ˆb. 1: Test H (1) 0 : S([ˆa, ˆb]) = 1 vs H (1) a : S([ˆa, ˆb]) < 1, using Dboot m . 2: if Accept H (1) 0 then 3: Test H (2) 0 : supp(S) is a single point vs H (2) a : supp(S) is not a single point using T boot m . 4: if Accept H (2) 0 the...

work page 2016

[7] [10]

Presumably this reflects Chinese manufacturing expertise of consumer 12 goods

we sees heavy doses of blue for the sectors consumer staples and consumer discretionary indicating these sectors are heavily dependent on other economic sectors. Presumably this reflects Chinese manufacturing expertise of consumer 12 goods. Despite these differences between the U.S. and China, both markets show some similarities in the utilities sector, w...

work page 1987

[8] [223]

Das, B. and S. Resnick (2017). Hidden regular variation under full and strong asymptotic depen- dence. Extremes 20 (4), 873–904. 15 Drees, H., A. Janßen, and Resnick, S.I., Wang, T. (2020). On a minimum distance procedure for threshold selection in tail analysis. Siam J. Math. Data Sci. 2 (1), 75–102. Drost, F. and T. Nijman (1993). Temporal aggregation o...

work page 2017