The Correlation Half-Life Survives the Contagion Network

The one number in this paper a risk manager should carry away is the DCC persistence. The directed network built on top of it is the part to leave behind. Pindza and Mba report a scalar DCC persistence of 0.9739 across twenty cryptocurrencies over 1,889 daily observations. Their sensitivity table varies panel breadth and regime. The implied half-life moves from 11.2 days at five assets to 38.8 at ten, and down to 9.2 days in the post-2022 subsample. The Hawkes side produces asset rankings from a 20x20 cross-excitation matrix, diagonal set to zero. Not one of the 380 estimated off-diagonal cells carries a standard error.

We have overlapping daily crypto history from 2021. Our coverage ends before March 2026, so we could not reproduce the paper's 2 January 2021 to 5 March 2026 panel. The paper's shock threshold, network cutoff and DCC quantities are all computed on the full sample. A tradable version would have to re-estimate them on rolling or expanding windows only. Nothing below is a test of the paper's method.

The subject is contagion across twenty coins at daily frequency, 1,889 log-return observations per asset. The universe is fixed by January 2021 market capitalisation, with stablecoins and wrapped tokens excluded. Two estimators run on the same return matrix. The first is a Hawkes self-exciting point process: one outsized daily move raises the probability of the next, and the effect decays exponentially. The second is a scalar DCC-GARCH (dynamic conditional correlation). It produces a mean pairwise conditional correlation, which the authors use as a market integration index.

What the authors report: MATIC, ATOM, ADA, SOL and ALGO as the strongest senders of excitation, and UNI as the dominant receiver. Persistence of 0.9739, a 26.2-day correlation half-life, four dated contagion episodes. There is no strategy in the paper, no portfolio and no P&L. So the money question is narrow. What does any of this change in a covariance engine or a stress test?

What they built

Pindza and Mba define an event as a day when the absolute log-return exceeds a threshold. The threshold is the asset's own full-sample mean plus two standard deviations of absolute returns. That gives 57 events for XLM up to 92 for BTC, mean 78 per asset. They fit mu, alpha and beta per asset by maximum likelihood. The ratio alpha/beta is the branching ratio: expected aftershocks per shock. VET tops out at 0.777, UNI bottoms at 0.311, cross-sectional mean 0.57. BTC and ETH both sit around 0.525.

The cross-asset layer works pair by pair. For each ordered pair they hold the target asset's univariate parameters fixed. Then they estimate a single cross-excitation coefficient alpha_ij from the source's event times. Do that 380 times and you have the matrix. Threshold the off-diagonal entries at the 90th percentile and you get a directed graph. MATIC has the highest out-degree at five outgoing edges. UNI has fifteen incoming edges and almost nothing going out.

Engle's scalar DCC-GARCH is fitted in two steps on the same twenty assets. Full-sample mean correlation 0.6754, standard deviation 0.0454, range 0.5249 to 0.7913. Sub-period means: 0.6303 in the 2021 bull, 0.7057 in the 2022 bear, 0.6699 in 2023, 0.6612 in 2024, 0.7047 from 2025 to March 2026. Episodes are contiguous runs above mean plus 1.5 sd, which is 0.744. There are four. Six days around the June 2021 China mining ban, peak 0.748. Thirty-three days for the collapse of LUNA/UST, the Terra stablecoin, peak 0.791. One day in April 2025 at 0.744. Seventeen days in October 2025, peak 0.780.

Data is daily USD closes from CryptoCompare.

The persistence result is the real one

Persistence of 0.9739 against the equity DCC benchmark the authors cite at 0.90 to 0.95, and government bonds near 0.85. The implied correlation half-life is 26.2 trading days. Their suggested response is an EWMA decay of 0.0261 per day, roughly 38.4 trading days of effective memory. A 60-day rolling covariance estimator will still be carrying pre-stress structure through the worst of the adjustment.

But check the sensitivity table before you write 26.2 into anything. Five-asset panel: a+b = 0.940, half-life 11.2 days. Ten-asset panel: 0.982, 38.8 days. Post-2022 subsample: 0.928, 9.2 days. The authors present this as showing the full-panel estimate is "not a purely mechanical artifact of the 20-asset dimension." The ordering does not support that reading cleanly. Persistence goes 0.940 at five assets, 0.982 at ten, 0.9739 at twenty. That is not monotone in panel size, which weakens the dimension story. Across the three panels the half-life still moves from 11.2 to 38.8 days, a factor of 3.5. The post-2022 subsample pushes it down to 9.2. Take the direction and discard the decimal.

The authors also flag that their window mixes post-pandemic liquidity, aggressive tightening and trade-policy shocks. They say the persistence figure may be an upper bound. They are right to say so. The 9.2-day post-2022 result is consistent with it.

Can a pairwise daily edge separate transmission from a common factor?

This is where the paper overreaches. The abstract states that "contagion transmission is led by medium-cap platform tokens." That claim is directional and causal. The estimator underneath it cannot carry it.

Start with what alpha_ij is. It is fitted for one ordered pair at a time. The target's univariate mu, alpha and beta are held at their previously estimated values. The target-side intensity in Eq. 5 is a baseline, plus self-excitation, plus one cross term. No common-factor component appears in it. So on a day when crypto sells off broadly, MATIC and UNI both cross their two-sigma bars. Whichever crosses first looks like the sender. With one observation per day there is no intraday ordering to break ties. The authors do argue for daily frequency rather than assume it: it suits institution-facing risk management, and it lets the Hawkes results sit alongside a DCC-GARCH estimated on the same data. The objection stands regardless.

The paper's own numbers hint at this. Mean pairwise correlation over the whole sample is 0.6754, never dropping below 0.5249. In a panel that integrated, most large absolute moves are the common factor. The Hawkes shock half-lives run 3.1 to 14.0 days, so events are not tightly clustered in time within an asset either.

And the matrix carries no standard errors, and no significance tests on any alpha_ij. There is no bootstrap or confidence interval on the network statistics. The reported inference is two Spearman rank tests. The edge set is the top decile of 380 numbers, and the roles are read off that. The sensitivity checks vary the cutoff across the 85th, 90th and 95th percentiles. MATIC keeps the largest out-degree at all three. Fine, but that tests threshold stability. It says nothing about whether the underlying coefficients differ from zero or from each other.

The authors do concede the structural point. Section 5.2 says the source and receiver labels "should therefore be read as economic roles in the shock-propagation network, not as fixed quality rankings of the projects." Section 5.4 calls the event labels "alignments rather than structural causal decompositions." The conclusion is weaker still: outgoing excitation strongest from MATIC, ATOM, ADA, SOL and ALGO, with UNI the dominant receiver. So why does the abstract say contagion transmission is led by medium-cap platform tokens, and name MATIC, ATOM, ADA and SOL as the strongest senders? The gap is between the abstract and everything else. The abstract is the part people will quote.

The result the abstract leaves out

Spearman correlation between weighted eigenvector centrality and in-degree is 0.64 with p = 0.002. Against out-degree it is weaker and insignificant. In-strength gives 0.50, p = 0.026. The paper's own phrasing is the best line in it: static centrality is more closely related to where contagion accumulates than to where it originates. The conclusion makes this the first of its three main results, and Section 6.2 develops it. The abstract omits it entirely. Strange allocation of space, given that this is the finding least vulnerable to the common-factor critique.

UNI illustrates it well. Lowest branching ratio in the panel at 0.3112. Highest baseline intensity at 0.0299. Fifteen incoming edges. Those three numbers describe a token whose shocks arrive from outside rather than feeding on themselves. Absorbing many incoming channels survives the common-factor critique better than direction does.

Two rank tests carry the network claim, p = 0.002 for in-degree and p = 0.026 for in-strength. No multiple-testing correction is reported.

Knife-edge dating, openly admitted

FTX, November 2022, reaches 0.738 against a threshold of 0.744. It does not register as an episode. Pindza and Mba report this openly and explain it. Correlations were already elevated, so a 1.5-sd rule computed on the full sample cannot flag it. They also note the January 2024 ETF approval month peaked at 0.657, nowhere near.

Read the whole of what they say about it, because they do not hide behind the rule. They call threshold rules "parsimonious dating devices rather than full narrative classifiers." Their sensitivity check loosens the cutoff to 1.25 sd, which pulls the FTX window in. Tightening it to 2.00 sd still retains LUNA and October 2025. An honest treatment of a fragile classifier.

What none of it changes: the threshold, like the shock indicator, uses full-sample moments. This dating could not have been produced in real time. The April 2025 one-day episode at exactly 0.744 is the clearest case. That crossing exists only because of where the full-sample mean and sd landed. The authors interpret it as transient common-factor repricing rather than a regime, which is the right call.

Where I would actually use this

Use it as a stress map. The volatility panel is the concrete piece. During the LUNA window BTC conditional volatility peaked at 0.24% daily and ETH at 0.28%. ADA hit 1.14%, XTZ 1.13% and ATOM 1.61%. ADA, XTZ and ATOM amplified the same LUNA shock while BTC peaked at 0.24%. That conclusion does not require the direction of any edge to be correct.

The correlation persistence goes into the covariance engine as a prior that post-stress reversion is slow. Use a range of 9 to 39 days rather than a point estimate of 26.2. There is no strategy here, no portfolio, no costs and no out-of-sample test. The 38.4-day EWMA memory is a suggestion derived from a fitted parameter. Nobody has tested it as a rule.

What would change my view on the network: a joint multivariate Hawkes fit with a common-factor component, standard errors on the cross-terms, and the sender ranking re-estimated on the post-2022 half. The authors themselves put full multivariate Hawkes estimation first in their list of future work. Until someone does it, MATIC as the market's contagion source is a description of a top-decile cell in a matrix. And BTC has 92 shock events, the highest count in the panel, on the lowest annualised volatility at 0.589. That is a reminder of how much the asset-specific threshold is doing.