Ecology's early warning of collapse misses stock market crashes
Lakes, forests and the climate recover more slowly from small shocks as they near a tipping point, and the 2009 Nature paper that made the idea famous counted financial markets among such systems. We tested its warning signal on 497 crash weeks in nine stock indices since 2000.
Can ecology’s early warning of collapse see a stock market crash coming?
Near a tipping point, the forces that pull a system back after a knock grow weak, so each day’s state looks more like the day before and the swings grow wider (Scheffer et al., 2009; Carpenter and Brock, 2006). In 2008 Vasilis Dakos and five colleagues found this slowing down in the climate record before each of eight abrupt shifts in the Earth’s past, starting well before the shift itself (Dakos et al., 2008). A year later Marten Scheffer and nine co-authors argued in Nature that it is a generic warning of tipping points in systems “ranging from ecosystems to financial markets and the climate” (Scheffer et al., 2009).
In a stock market the knocks are the daily returns, so a market losing its resilience would show rising autocorrelation, each day’s return growing more like the day before, in the months ahead of a crash. We call a crash week a calendar week in which an index’s lowest close falls at least 5% below its last close of the week before. Since 2000 the S&P 500 has had 46 crash weeks, and nine indices in North America, Europe, Asia and Australia have had 497 between them. A warning that flags 30% of weeks at random catches 30% of crash weeks on average, so a warning is worth what it catches above the share of weeks it flags.
Rising autocorrelation caught about as many crash weeks as chance would. On the S&P 500 it flagged 16 of 46, where a random flag raised as often would catch 14 (Fig. 1). Across all nine indices it did worse than chance, with 135 crash weeks caught against the 158 a random flag would catch. The VIX, Cboe’s measure of the volatility priced into S&P 500 options, flagged about as many weeks and caught 38 of the 46, more than twice as many as the slowing-down signal. Stock markets crash out of turbulence, and turbulence lowers the autocorrelation the warning looks for.
The VIX caught 38 of the S&P 500's 46 crash weeks, and rising autocorrelation about as many as a random flag would.
Share of the S&P 500's crash weeks since 2000 that each gauge flagged at the close before (red dot), against the share a random flag raised as often would catch (ring).
Rising autocorrelation flagged the S&P 500’s crashes at the rate of chance
The slowing-down signal reads the S&P 500 the way ecologists read a lake or a climate record (Dakos et al., 2012). It takes the correlation between each day’s return and the day before over the last 60 trading days, then scores that correlation’s trend over the last 120 days with Kendall’s rank correlation against time (Kendall, 1938). A score of +1 means the autocorrelation rose every day for six months, and 0 means no trend. Each return is first divided by its recent volatility, so a calm month and a wild one count alike.
The signal flags the coming week when its score is above 0.244, a line set so that it flagged 30% of the S&P 500’s weeks from 1962 to 1999. Since 2000 it has flagged 16 of the 46 crash weeks, about two more than a random flag raised as often would. Luck alone often does as well. Sliding the signal’s record in time by a year or more keeps its flags as bunched as before but out of step with the crashes, and more than a third of those slides caught 16 or more.
Ecologists usually read rising autocorrelation together with rising variance, the wider swings of a system near its tipping point, and that classic pair did better. It caught 23 of the 46 crash weeks, where chance would catch 15, and only 5% of the slides did as well. The variance carried it. On its own, rising variance caught 19 crash weeks against 13 by chance, while rising autocorrelation of the raw returns caught 14 against 15.
Rising variance in a stock index is what traders call rising volatility, and volatility comes in clusters. In nine stock indices, big moves came on 16.9% of days in the third to sixth weeks after a one-day shock, almost three times the ordinary rate (ATOL, 2026). A gauge that reads volatility directly catches those clusters without waiting for a six-month trend. Recent swings, the volatility of the last 20 days against its median over the past year, caught 35 of the 46 crash weeks (Fig. 1).
Across nine stock markets the slowing-down signal caught fewer crashes than a random flag
The same signal, with the same line, ran on eight more indices: the S&P/TSX Composite, the FTSE 100, the Nikkei 225, the Hang Seng, the Dow Jones Industrial Average, the DAX, the S&P/ASX 200 and the Euro Stoxx 50. Since 2000 they have had between 27 crash weeks, in the S&P/ASX 200, and 91, in the Hang Seng.
Of the 497 crash weeks in all nine indices, the signal caught 135, where a random flag raised as often would catch 158 (Fig. 2). It fell short of chance in five of the nine. In the Dow it caught 5 of 37 crash weeks, and in the Nikkei 225 it caught 13 of 84, in each case under half of what a random flag would catch. Crashes strike several markets in the same week, so the test also slid the nine indices’ flags in time together. Those slides averaged 154 catches, and fewer than one in five did as badly as the signal’s 135.
Rising autocorrelation caught fewer crash weeks than a random flag in five of nine stock indices, and in all nine together.
Share of each index's crash weeks since 2000 that the signal flagged at the close before (red dot), against the share a random flag raised as often would catch (ring).
Each market’s own recent swings did far better, with nothing to go on but its daily closes. With its line drawn the same way, on the S&P 500 before 2000, the recent-swings gauge caught 298 of the 497 crash weeks, almost twice the 152 a random flag would catch. The classic pair caught 184, a little more than the 165 of chance. The VIX, read for all nine as a gauge of fear in the world’s largest market, caught 347, more than twice the 150 of a random flag.
Stock markets crash out of storms, and storms wash out the slowing down
A crash week rarely comes out of calm. Since 2000 the VIX has closed above its median of the past year in about four weeks out of ten, yet it stood there at the close before 43 of the S&P 500’s 46 crash weeks. Recent swings stood above their median before 39 of them.
Turbulence works against the slowing-down signal. LeBaron (1992) documented the reason in US indices: the more turbulent the market, the lower the autocorrelation of its daily returns. In calm markets each day’s move leans slightly the same way as the day before, while in storms it leans slightly the other way. Ranked by the volatility of the 20 days before, the S&P 500’s trading days since 1962 show the correlation between one day’s return and the next falling from 0.13 in the calmest fifth to -0.07 in the stormiest (Fig. 3). In the stormiest fifth of days since 2000 it reached -0.145. As a storm builds, returns grow less alike from one day to the next, the reverse of what the slowing down before a tipping point would produce.
The stormier the S&P 500, the less each day's return resembles the day before.
Correlation between one day's return and the next, in five equal groups of the 16,267 trading days since 1962 ranked by the volatility of the 20 days before, which averaged 7% a year in the calmest fifth and 26% in the stormiest.
The autumn of 2008 shows the effect at full size. The S&P 500 had nine crash weeks from September to December, the worst starting October 6, when its lowest close was 18.2% below the Friday before. Through September the slowing-down signal stood near -0.6, the score of an autocorrelation falling week after week, and it flagged none of the nine (Fig. 4). The VIX flagged all nine. The signal climbed back above its line on December 19, 2008, after the worst weeks had passed, and flagged the four crash weeks of early 2009, which the VIX also flagged.
The slowing-down signal pointed down through the nine crash weeks of autumn 2008 and crossed its flag line only after the worst had passed.
The signal's score, the trend in the S&P 500's autocorrelation, at each week's last close from January 2008 to June 2009; the dashed verticals mark the start of each crash week.
Guttal et al. (2016) found the same pattern in a century of crashes in the Dow, the S&P 500, the Nasdaq, the DAX and the FTSE 100: no rise in autocorrelation before them, and strong rises in variance. They concluded that crashes are likely stochastic transitions, which growing shocks can set off even in a market far from any tipping point.
The VIX caught 38 of the 46 crash weeks, and most first crashes of a storm
Option prices flagged most of the crashes. Whaley (2000) named the VIX the investor fear gauge, and Cboe describes it as a measure of the near-term volatility that S&P 500 option prices expect (Cboe, 2026a). As a gauge here it flags a week when it closes about 10% above its median of the past year, a line it crossed in 30% of weeks in the 1990s. Since 2000 it has caught 38 of the 46 crash weeks, almost three times the 14 a random flag raised as often would catch.
The result holds wherever the lines sit. Forced to flag the same share of weeks, anywhere from 10% to 50%, the VIX caught more crash weeks than the slowing-down signal at every share (Fig. 5). When each gauge flagged only its highest tenth of weeks, the VIX caught 19 crash weeks and the signal 2, and at 30% of weeks the count was 38 to 14.
Flagging the same share of weeks, the VIX caught more S&P 500 crash weeks than the slowing-down signal at every share.
Share of the S&P 500's 46 crash weeks since 2000 caught when each gauge flags its highest 10% to 50% of weeks: the VIX (red dot), rising autocorrelation (black dot) and a random flag (ring).
The harder test is the first crash week of a storm. One crash week often follows another, so much of any gauge’s record comes from storms already under way, and the S&P 500 had 18 crash weeks with no other in the 13 weeks before (Table 1). The VIX caught 11 of them, twice what chance would, against 8 for recent swings and 4 for rising autocorrelation. Option prices flagged more of these first crashes than any reading of the closes.
Table 1. The VIX caught 11 of the S&P 500’s 18 first crash weeks of a storm, and rising autocorrelation caught 4.
| Gauge | Weeks flagged | First crash weeks caught | Caught by a random flag |
|---|---|---|---|
| VIX against its one-year median | 30.1% | 11 of 18 | 5.4 |
| Recent swings against their one-year median | 32.5% | 8 of 18 | 5.8 |
| Rising variance and autocorrelation | 33.2% | 6 of 18 | 6.0 |
| Rising autocorrelation | 30.6% | 4 of 18 | 5.5 |
Three crash weeks came out of calm markets and every gauge missed them: the weeks starting October 9, 2000, August 17, 2015 and October 26, 2020.
The slowing down did appear before Black Monday, and rising variance carries a warning
The best case for the signal is 1987. Diks, Hommes and Wang (2019) tested four crises: Black Monday in October 1987, the Asian crisis of 1997, the end of the dot-com bubble in 2000 and the crisis of 2008. They found statistical evidence of critical slowing down before Black Monday, and mixed or insignificant results for the other three. The signal here agrees on 1987: it stood above its line for 15 straight weeks, from July 10 to October 16, 1987, before the week of Black Monday, when the S&P 500 closed 20.5% below that Friday.
One hit is a short record. Over 1963 to 1999 as a whole the signal caught 11 of the S&P 500’s 27 crash weeks, about three more than chance, a margin that one slide in four matches. Recent swings caught 21 of the same 27, and flagged Black Monday too, standing at twice their median on October 16, 1987.
The second case is rising variance, which Guttal et al. (2016) offered as a precursor of crashes, false alarms and all. The S&P 500 bears them out: the classic pair, carried by its variance half, caught 23 of the 46 crash weeks, half as many again as chance. A trend in variance is a slow reading of volatility, though, and the gauges that read volatility directly caught more, 35 for recent swings and 38 for the VIX. Across the nine indices the classic pair caught 184 crash weeks, against 165 for a random flag and 298 for recent swings.
What to watch
At the September 18, 2026 close no gauge flagged the coming week. Rising autocorrelation stood at 0.01, far below its line of 0.244, and the classic pair was negative, at -0.34. Recent swings ran at about three quarters of their one-year median, short of their line. The VIX closed at 14.81, below its one-year median of 17.24, and needed a close above 18.90 to flag a week. On October 2 it closed at 15.31, against a line that had eased to 18.86 (Cboe, 2026b).
Two results would bring the slowing-down signal back. A crash week preceded by months of rising autocorrelation in several of the nine indices at once, with the signal above 0.244, would repeat the pattern of 1987. A run of crash weeks out of calm markets that the signal flags and the VIX misses, like the three that every gauge missed here, would show the signal seeing something the fear gauge cannot.
How we got the number
The information set and its dates
The test uses daily closing levels of nine stock indices, each from the start of its history in the source, January 2, 1962 for the S&P 500, to September 21, 2026. The Nikkei 225 ends on September 18, since September 21 was a holiday in Japan. The closes were retrieved from Yahoo Finance on September 26, 2026; the S&P 500, Dow and Nikkei 225 closes agree with FRED’s copies of the publishers’ series within 0.12% on every shared day (ATOL, 2026). The VIX is Cboe’s daily history from January 2, 1990 to October 2, 2026, downloaded from Cboe on October 5, 2026 (Cboe, 2026b).
The test weeks run from the week starting January 3, 2000 to the week ending September 18, 2026: 1,394 for the S&P 500 and 12,001 index-weeks in all, fewer where an index’s history starts later. “Since 2000” in the story means these weeks. Each gauge is read at the last close of a week and judged on the week that follows, so no gauge sees the week it flags. The lines were drawn on the S&P 500’s weeks up to December 31, 1999, and no crash week entered the drawing of any line.
The calculation
With $P_t$ the close on day $t$, the daily log return is $r_t$, and the slowing-down signal first scales it by an exponentially weighted volatility $\sigma_t$ built from returns up to the day before, with the decay $\lambda = 0.94$ that RiskMetrics set for daily data (J.P. Morgan and Reuters, 1996).
The indicator is the lag-1 autocorrelation of a series $x$ over the last 60 trading days, and the gauge is that indicator’s trend over the last 120 trading days, measured by Kendall’s $\tau$ against time (Dakos et al., 2012; Kendall, 1938).
Rising autocorrelation is $T_t$ of the autocorrelation of $z$. The classic pair averages the trend of the 60-day variance of $r$ and the trend of the autocorrelation of the unscaled returns $r$.
Recent swings divides the standard deviation of the last 20 daily returns, $s_t$, by its median over the last 252 trading days, and the VIX gauge divides the VIX close by its median over the last 252 closes.
Each gauge flags the week after day $t$ when its reading is at or above its line $q$, the 70th percentile of its readings at the last close of each S&P 500 week up to 1999 (Table 2). Week $w+1$ is a crash week when its lowest close falls at least 5% below the last close of week $w$.
Table 2. Each gauge’s line, drawn on the S&P 500’s weeks before 2000.
| Gauge | Line | S&P 500 weeks used |
|---|---|---|
| Rising autocorrelation, $V^{(1)}$ | 0.244 | 1,934, December 1962 to December 1999 |
| Rising variance and autocorrelation, $V^{(2)}$ | 0.135 | 1,946, September 1962 to December 1999 |
| Recent swings, $S$ | 1.175 | 1,928, January 1963 to December 1999 |
| VIX against its median, $R$ | 1.096 | 471, December 1990 to December 1999 |
A gauge that flags a share $f$ of $n$ weeks holding $c$ crash weeks catches $k$ of them, and a random flag at the same rate catches $cf$ on average (Eq. 6). Flags cluster in time and so do crash weeks, so the slide test moves the gauge’s whole record of flags against the crash weeks by every offset $j$ from 52 weeks to $n-52$, wrapping at the ends, and reports the share of offsets that catch at least $k$ (Eq. 7). For the nine indices the flags of all nine move together, which keeps crashes that strike several markets in one week together.
Figure 5 drops the lines and lets each gauge flag its highest 10% to 50% of test weeks. Table 1’s first crash weeks are crash weeks with none in the 13 weeks before, counted over the S&P 500’s whole history. Figure 3 ranks every S&P 500 day from 1962 by the standard deviation of the 20 returns before it, splits the days into five equal groups and correlates each day’s return with the day before within each group.
Limitations
- The test uses closes only. A crash week defined on intraday lows would add weeks in which an index fell 5% during a day and recovered by the close.
- The signal uses one choice of windows, 60 days for the autocorrelation and 120 for its trend, and one line, the 70th percentile. Figure 5 shows the ranking holds at every flag share from 10% to 50%; other windows are the next check.
- The crash line is 5%. Moving it to 4%, 6% or 7% keeps the ordering: across the nine indices rising autocorrelation caught fewer crash weeks than chance at each line (270 against 282.3, 84 against 93.3, 49 against 58.3), and the VIX at least twice as many as chance (546, 229 and 155).
- The nine indices overlap, the Dow with the S&P 500 and the DAX with the Euro Stoxx 50, and crash weeks cluster, so the 497 hold fewer independent events than the count suggests. The slide test keeps both kinds of clustering, and its spread is the error band to read.
- The two slowing-down gauges and the 70th-percentile rule come from an earlier ATOL test, run on September 26, 2026 against a different set of S&P 500 crash weeks. The 5% crash line, the recent-swings gauge and the nine-index test were fixed before any gauge was scored against them, and the paper is exploratory.
- The signal is read on daily index returns. Slowing down could still show in other series, such as credit spreads or bank funding rates, which this test does not cover.
Reproducing it
The analysis runs offline in Python 3.12 with NumPy, pandas, SciPy and PyYAML. It rebuilds every figure and every number quoted here from the sources in the information set above, the index closes and the VIX history included.
References
- Atol Research. (2026). What stock markets do in the weeks after a crash. RPT-004, October 5.
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- Cboe Global Markets. (2022). Terms and conditions for use of Cboe websites. Last updated November 16, 2022.
- Cboe Global Markets. (2026a). VIX Index. Read October 5, 2026.
- Cboe Global Markets. (2026b). Historical data for Cboe VIX Index and other volatility indices. VIX_History.csv, read October 5, 2026.
- Dakos, V., Carpenter, S. R., Brock, W. A., Ellison, A. M., Guttal, V., Ives, A. R., Kéfi, S., Livina, V., Seekell, D. A., van Nes, E. H., and Scheffer, M. (2012). Methods for detecting early warnings of critical transitions in time series illustrated using simulated ecological data. PLoS ONE, 7(7), e41010.
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- J.P. Morgan and Reuters. (1996). RiskMetrics Technical Document. Fourth edition, New York.
- Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1/2), 81 to 93.
- LeBaron, B. (1992). Some relations between volatility and serial correlations in stock market returns. The Journal of Business, 65(2), 199 to 219.
- Scheffer, M., Bascompte, J., Brock, W. A., Brovkin, V., Carpenter, S. R., Dakos, V., et al. (2009). Early-warning signals for critical transitions. Nature, 461(7260), 53 to 59.
- Whaley, R. E. (2000). The investor fear gauge. The Journal of Portfolio Management, 26(3), 12 to 17.