Only 6.10 of this paper's connectedness points offer even the possibility of a lead-lag signal across oil, defence, tech and Bitcoin. The total connectedness index is 48.93%. Its remaining 42.83 points measure same-day co-movement, already gone by the time a trader can observe it. The authors acknowledge this. They find that contemporaneous effects dominate and interpret that dominance as information entering prices quickly. Our contribution is to locate the residual: about half of the 6.10 falls in the Nikkei 225 and STOXX 600 rows, where different closing times could account for it.

Reading the R² map

Belhouichet, Caporale and Gil-Alana use nine daily log-return series covering 1 January 2023 to 22 September 2025, with 996 observations. Their universe contains three sector ETFs (XLE for energy, ITA for defence, XLK for technology), Bitcoin, the S&P 500, the Nikkei 225, the STOXX 600, Brent crude, and the Caldara-Iacoviello geopolitical risk (GPR) index. They apply the R²-decomposed connectedness method of Balli et al. (2023), which divides each regression's explanatory power among its inputs. Each series' return is regressed on the other eight series' same-day returns and one lag of all nine. BIC selects the lag order of one. A PCA rotation orthogonalises the regressors, allowing the R² to be divided into additive contributions from each regressor to the target.

The contributions are then summed. TO measures how much a series explains in the other regressions; FROM measures how much the others explain of that series. Subtracting FROM from TO gives NET. A positive NET earns the label "net transmitter". The total connectedness index (TCI) averages the R² across the nine regressions. The estimates use 200-day rolling windows and are then averaged. For investors, the proposed reading is that the contemporaneous share measures how quickly diversification fails, and the lagged share measures the time available to rebalance.

The S&P 500 leads the transmitter ranking with NET +21.11%, comprising TO 110.79% and FROM 89.68%. The largest receivers are the Nikkei (−11.50%), Brent (−9.27%) and the STOXX 600 (−4.06%). Much of the table comes down to two pairs. The S&P 500 explains 59.10% of XLK; in the reverse regression, XLK explains 52.62% of the S&P 500. For XLE and Brent, the corresponding figures are 33.59% and 28.68%.

Where does the 6.10 go?

Lagged R² measures in-sample fit within each 200-day window. Although the methods section says the results are tested through cross-validation, we found no reported cross-validated or out-of-sample result. We also found no portfolio test. The paper reports no forecast evaluation for the lagged share.

Two rows account for about half of it.

The Nikkei's NET of −11.50% comprises a lagged −10.82% and a contemporaneous −0.68%. Its lagged FROM reaches 16.65%, including 4.21 from the S&P 500 and 5.39 from XLK. Tokyo closes before New York opens. Yesterday's US close therefore supplies today's news in Japan. The STOXX 600 closes during the New York session and has lagged FROM of 10.26%. Those rows together account for 26.91 of the 54.88 lagged points, or about 49%. We found no description of the authors' treatment of trading-calendar alignment.

The lag-order check raises another problem. With two lags, TCI rises to 50.64%. The contemporaneous component changes little, moving from 42.83% to 41.89%, while the lagged component climbs from 6.10% to 8.75%. Adding a lag increases it by 43%. The authors report this increase and interpret it as additional lagged interaction. They regard the main findings as confirmed, a reading that holds for the transmitter ranking. The component a trader would care about, though, is the one least pinned down by the specification.

The S&P 500's claim to direction

Contemporaneous effects account for NET +15.62% of the S&P 500's +21.11% lead. Same-day R² supplies no time order. "Direction" reflects only which regression a variable contributes more to, and an index correlated with every equity node will accumulate TO. The mutual explanatory shares of 59.10% and 52.62% for the S&P 500 and XLK look like shared holdings.

XLK and ITA are small net transmitters in the total network, with NET +2.16% and +0.74%. Restrict the network to same-day effects and they become receivers, at −3.83% and −2.82%, from the index that holds them. The abstract places ITA and XLK next after the S&P 500 among emitters. Yet Table 2 ranks XLE (+2.60%) above both, and ITA changes sign to −0.10% with two lags. The authors acknowledge that the method alone cannot capture the economic mechanisms, while maintaining that it identifies direction and timing. Direction remains doubtful for the 15.62 contemporaneous points in the S&P 500's lead. That doubt warrants more weight than the abstract's description of the S&P 500 as the "main shock emitter".

Bitcoin's small footprint says something about correlation

The paper judges Bitcoin's safe-haven role to be limited. Its evidence is unconditional connectedness: FROM 19.07%, TO 17.52%, NET −1.55%. Bitcoin's return variance, meanwhile, is 6.060, compared with 0.642 for the S&P 500, about 9.4 times as large. High variance alongside low R² describes idiosyncratic risk. A haven judgement, even "limited", requires conditioning on equity drawdowns. We found no stress-conditional test. Unconditional connectedness alone leaves the question open in both directions.

GPR has an even weaker position, despite geopolitical risk appearing in the paper's title. It records FROM 6.99%, TO 6.76% and NET +0.23%. Its own lag, at 10.45, is the largest entry in its row. The authors draw attention to this and propose that geopolitical effects may pass indirectly through oil and sentiment. They also present the event links in their dynamic charts as plausible economic contexts rather than causal explanations. GPR's variance is 2530.28. The paper's single return formula suggests that the news index was log-differenced like a price. If so, it may simply register as noise elsewhere in the system.

Before trusting the map, check the inputs

The inclusive period from 1 January 2023 to 22 September 2025 contains exactly 996 calendar days. Seven exchange-traded series, the three ETFs, the S&P 500, the Nikkei 225, the STOXX 600 and Brent, have no weekend prints. We therefore infer filled or stale prices. Stale zeros lower same-day correlation and can create apparent lags, a concern that bears directly on the 6.10. Several other details fail to reconcile:

We could not reconstruct the network. Our data contains neither a Brent series nor the Caldara-Iacoviello index, and we cannot confirm coverage of the Nikkei 225 and STOXX 600 themselves. Using WTI or US-listed index ETFs instead would test a different system. A Japan ETF trading during New York hours would also remove the closing-time gap that we suspect accounts for the Nikkei's lagged role.

The paper offers a fair map of same-day correlation among overlapping US equity exposures, alongside an oil-and-energy-equity pair. I would accept the lagged share as a signal only after it passes two tests: aligning closes to a common timestamp, and scoring a forecast on data unseen by the 200-day windows. The paper mentions the latter through cross-validation, but never reports it.