Cointegration as Regime, Not State

(1) Executive Summary

Most investors who encounter Cointegration encounter it as a yes-or-no question. Are these two assets cointegrated? Run an Engle-Granger test, get a p-value, declare the relationship valid or invalid, and move on. This treatment of Cointegration as a binary state is the single most common methodological error in applied financial statistics — and it produces conclusions that are simultaneously over-confident in their precision and under-informative about what is actually happening in markets.

Cointegration is a regime, not a state. Markets cycle through phases where statistical relationships hold and phases where they break. The right question is not "is this pair cointegrated" but rather: "in what fraction of historical windows does the relationship hold, what triggers regime transitions, and what is the current regime telling us about the macro environment?"

This Lab Read formalizes that framing. We test the regime-based methodology on two structurally different pairs. BTC versus Gold tests the substitution thesis: when capital rotates between Store-of-Value assets, the spread between them is mean-reverting and statistically stationary; when both assets trade on independent narratives, the relationship breaks. BTC versus NDX (proxied by QQQ) tests the lead-lag thesis: when crypto-native sentiment leads institutional risk-on positioning, BTC moves first and NDX follows in a measurable lag window; when the lead breaks down, BTC trades on its own halving-cycle dynamics independent of tech beta. Both pairs have statistically distinguishable On-regimes and Off-regimes, and the alternation between the two regimes is itself the macroeconomic signal.

We document the methodology, walk through the two thesis cases, and close with the joint reading: combining both pairs into a 2x2 Macro-Quadrant framework that classifies the current market mode in real time.

The honest framing throughout: nothing is permanent in markets. Relationships hold sometimes and break sometimes, and the value of the methodology is precisely in detecting which mode we are in, not in declaring permanent truths.

(2) Why Cointegration Matters For Closelook Readers

Closelook readers already know the limits of correlation. Two assets can be correlated for six months because they happen to be moving in the same direction; correlation tells you nothing about whether the relationship will persist. Investors who confuse correlation with structural connection get blindsided when the relationship breaks, because correlation does not contain information about why two assets move together.

Cointegration is the upgrade. Two assets are cointegrated when there exists a linear combination of them — a spread — that is statistically mean-reverting. This is a much stronger claim than correlation. It says that even if both assets wander individually over long horizons, the distance between them snaps back to a long-run equilibrium. There is a tether. The two assets share a deeper structural connection that produces stationary deviations from a common path.

For Closelook readers familiar with the Money Temperature framework, this is the same logic applied to a different question. Temperature asks: "what is the current macro regime?" Cointegration asks: "which two assets are currently sharing a structural tether, and what does that tether tell us about the macro regime?" Together they form complementary readings — Temperature reads the macro from one direction, Cointegration reads it from another, and when both agree, the conviction level of the macro thesis is much higher.

The Pattern Lab houses both. The Pattern Engine surfaces the live signals. This Lab Read is the methodological foundation underneath the Cointegration Monitor that you can already see operating at closelook.net/lab/cointegration/.

(3) The Statistics — Two Method Families

The statistical apparatus we need divides cleanly into two method families. The first family addresses the basic question of whether a relationship exists at any given moment. The second family addresses the more subtle question of whether one asset leads the other in time. Both families are needed because the two pairs we test demand different methodological treatment.

Family One — Cointegration Detection

The foundational test for cointegration is the Engle-Granger two-step procedure, published in 1987. Step one regresses one asset on the other to extract the residual spread. Step two applies the Augmented Dickey-Fuller test to the residual to assess whether it is stationary. If the residual is stationary, the two assets share a long-run equilibrium and are said to be cointegrated. If the residual itself wanders without reverting, the two assets are not cointegrated and any apparent correlation is coincidental.

The Augmented Dickey-Fuller test is a statistical hypothesis test where the null hypothesis is non-stationarity. Rejecting the null at conventional thresholds, typically a p-value below 0.05, allows us to conclude that the residual is stationary. The test itself is technical in implementation but conceptually simple: we ask whether mean reversion is a real feature of the data or just a pattern that could plausibly emerge from random walk noise.

Around this core test, two supporting metrics provide additional information.

The Hurst Exponent measures whether a time series is mean-reverting, random-walking, or trending. A Hurst value below 0.5 indicates mean reversion, around 0.5 indicates random walk behavior, and above 0.5 indicates trending behavior. Applied to a spread, the Hurst Exponent gives us a continuous measure of how strongly mean-reverting the spread is, which is more informative than the binary stationary-or-not output of the ADF test.

The Halflife of mean reversion measures how long it takes a spread to revert halfway back to its long-run mean. If the spread is one standard deviation away from equilibrium, the halflife tells us how many trading days are expected to pass before the spread is half a standard deviation away. A short halflife indicates a tightly tethered pair; a long halflife indicates a loose tether that may not be tradable in practice. The Halflife is computed by fitting an Ornstein-Uhlenbeck mean-reversion model to the spread, treating the spread as a continuous mean-reverting stochastic process and extracting the reversion-rate parameter from which the halflife follows directly. This is the methodologically standard approach in stat-arb literature and produces a more stable estimate than the simpler discrete autoregressive approximation.

Family Two — Lead-Lag Analysis

When two assets are cointegrated and we want to know which one moves first, we need a different methodological apparatus. Cointegration tells us that a relationship exists. Lead-lag analysis tells us about the temporal structure of that relationship.

The primary tool is the Cross-Correlation Function, which computes the correlation between two time series at various lag values. If asset A at time t is more correlated with asset B at time t+2 than with asset B at time t+0, then asset A leads asset B by approximately two periods. The peak of the Cross-Correlation Function identifies the dominant lead-lag relationship.

In financial data, the peak is rarely a sharp spike at a single lag. It is typically a plateau spanning several adjacent lags. This means the honest reporting of a lead-lag relationship is a range, not a point estimate. Saying "BTC leads NDX by exactly two days" implies a precision the data does not support. Saying "BTC leads NDX in a window of one to four trading days, with the strongest cross-correlation typically observed at lag two to three" reflects what the data actually shows. Throughout this Lab Read we report lead-lag relationships as ranges and resist the temptation to collapse them to single numbers.

The Granger Causality test formalizes the lead-lag question statistically. It asks whether past values of asset A help predict future values of asset B beyond what past values of asset B alone can predict. If yes, A is said to Granger-cause B. The Granger test is a hypothesis test with a p-value, and the same regime-based logic applies: in some windows A Granger-causes B, in other windows the relationship is bidirectional or absent.

Combining cointegration and Granger causality produces what econometricians call a Vector Error Correction Model. We do not formalize the model in this Lab Read, but the conceptual content is straightforward: when a cointegrated spread deviates from equilibrium, both assets adjust back toward equilibrium at potentially different speeds, and the adjustment speed asymmetry is what we observe as lead-lag.

Why The Static Test Is Wrong

Both families share a critical limitation when applied as single-sample tests over long historical windows. A single-sample test asks: "averaged over the entire 2018-2026 period, are these assets cointegrated?" The answer is almost always either a definitive yes or a definitive no — and either answer is misleading.

The reason is that markets transition between regimes. In some periods, BTC and Gold trade on a substitution dynamic and the spread is stationary. In other periods, BTC trades on a halving-cycle dynamic and Gold trades on a real-rates dynamic, and the spread wanders. Averaging across both periods produces a number that is true on average but useful in neither regime.

The methodological fix is the rolling window. Instead of testing once over the full sample, we test continuously over rolling 180-trading-day windows. Each day, we compute the Engle-Granger p-value for the trailing 180 days. The output is not a number but a time series. We can then identify which periods showed statistically significant cointegration (rolling p-value below 0.05) and which did not. We can count regime durations, identify transitions, and compute the fraction of historical time in which the relationship held.

This rolling approach is the methodological backbone of everything that follows.

(4) Why Cointegration Is Different From Correlation

Before proceeding to the worked theses, one more conceptual distinction is worth making explicit because it is the most common source of confusion. Correlation and cointegration measure different things, and conflating them produces persistently bad inference.

Correlation measures whether two assets tend to move in the same direction over a given window. If both assets gained ten percent over the past quarter, they are positively correlated for that quarter regardless of whether they are structurally connected. Correlation is a measurement of co-movement.

Cointegration measures whether two assets share a long-run equilibrium relationship even if their short-term movements diverge. Two cointegrated assets can have low correlation in any given week and still be cointegrated overall, because the cointegration is about the spread reverting to a stable relationship over longer horizons. Two highly correlated assets can fail to be cointegrated, because their correlation may be a coincidental result of both responding to the same external factor without sharing a structural tether.

The practical implication is that correlation analysis fails precisely when investors most need it to work — during regime transitions and structural breaks. When two assets that have been correlated for six months suddenly diverge, the correlation framework provides no warning and no explanation. Cointegration analysis, by contrast, can detect the early signs of a regime transition through the gradual breakdown of the spread's stationarity properties. The Hurst Exponent rises before the regime breaks. The halflife extends. The rolling ADF p-value drifts upward through the threshold. These are observable signals that a regime transition is in progress, and they have no analog in correlation analysis.

This is why Cointegration belongs in a methodological Lab Read and Correlation does not. Correlation is a measurement. Cointegration is a methodology that produces both measurements and forward-looking signals.

(5) The Mechanic — How The Cointegration Monitor Computes Regimes

The Closelook Cointegration Monitor implements the rolling-window methodology described above as a continuous pipeline. The pipeline runs every trading day and produces, for each tested pair, a current regime classification, a continuous strength metric, a Halflife estimate, and a Hurst Exponent reading. The output is published to closelook.net/lab/cointegration/ and is updated automatically as new daily data arrives.

The pipeline has five steps.

The first step is data ingestion. EODHD daily closing prices for both legs of the pair are pulled and aligned to common trading calendars. For BTC, we use the BTC-USD pair as the canonical reference. For Gold, we use the GLD ETF as a tradable proxy with longer reliable history than spot gold contracts. For NDX, we use the QQQ ETF as the standard tradable proxy. All series are pulled from 2018 onward, providing eight years of daily history at any given publication date. Logarithmic transforms are applied to all price series to stabilize variance and facilitate the regression that follows.

The second step is rolling-window spread construction. For each trailing 180-trading-day window, the engine runs an ordinary least squares regression of the first leg on the second leg, extracts the residual time series, and stores it as the candidate spread for that window. The 180-day choice is the methodological default and is sensitivity-tested against 90-day and 252-day windows in the underlying calibration; the results are qualitatively robust across the three choices but the 180-day window provides the cleanest balance of regime sensitivity and statistical stability.

The third step is regime classification. For each rolling-window spread, the engine runs the Augmented Dickey-Fuller test and records the p-value. If p is below 0.05, the window is classified as an On-regime: cointegrated, mean-reverting, structurally tethered. If p is above 0.10, the window is classified as an Off-regime: not cointegrated, no statistically detectable tether. If p falls between 0.05 and 0.10, the window is classified as a Transition-regime: ambiguous, drifting between coupled and decoupled, signal-quality marginal.

The fourth step is supplementary metric computation. For each rolling window, regardless of regime classification, the engine computes the Hurst Exponent and the Halflife of mean reversion. These are stored alongside the regime classification and made available for downstream consumption. The Hurst Exponent is particularly valuable as an early-warning indicator: a Hurst that drifts upward from below 0.5 toward 0.5 within an On-regime is a leading sign that the regime is weakening, even if the ADF p-value has not yet crossed the threshold.

The fifth step is publishing. The engine writes the current regime classification, all supplementary metrics, the spread time series, and a short text interpretation to the Cointegration Monitor at closelook.net/lab/cointegration/. The published output is a snapshot of the current state plus the rolling history, allowing readers to see both where the relationship is now and how it has evolved over the years.

For BTC/NDX specifically, an additional sub-pipeline runs the lead-lag analysis. For each rolling window classified as On-regime, the engine computes the Cross-Correlation Function between the two assets at lags ranging from minus ten to plus ten trading days, identifies the peak lag, and identifies the plateau range — all lags where the cross-correlation exceeds ninety percent of the peak value. The output is a lead-lag range that updates daily and is cross-referenced against the regime classification.

(6) The First Thesis — BTC and Gold as Substitution Pair

The BTC/Gold pair is the classical Store-of-Value question made statistical. The intuition: if Bitcoin truly is "digital gold," then capital seeking inflation hedges and currency-debasement protection should rotate between the two assets based on relative attractiveness — when Gold rallies, BTC sees outflows; when BTC rallies, Gold sees outflows. This rotation produces a statistically stationary spread and registers as cointegration in our methodology. If, on the other hand, Bitcoin is fundamentally a different kind of asset — a tech-adjacent risk-on play, a halving-cycle phenomenon, a speculative momentum vehicle — then the substitution dynamic does not hold and the spread wanders without statistical tether.

The methodological case for this pair is clean for three reasons.

First, the substitution dynamic when it operates is interpretable. We are not searching for a statistical pattern of unknown origin. We have a theory: capital rotates between Store-of-Value assets based on relative attractiveness, and when this rotation is active the two assets share a structural tether. The rolling cointegration test either confirms or rejects this theory at any given moment, and the answer is informative regardless of which way it resolves.

Second, the regime durations are economically meaningful. When the test classifies a period as cointegrated, the typical duration of that On-regime is several months to over a year. This is long enough to be tradable, long enough to be macro-relevant, and long enough to outlast typical correlation-based pseudo-relationships that emerge from random co-movement.

Third, regime transitions are rich in information. When a long-running On-regime breaks and the spread starts wandering, that transition is itself a macro signal. It tells us that the substitution dynamic has been suspended, which usually means one of the two assets has acquired a new dominant driver — a halving cycle, a real-rates shock, a flight to safety, a new capital flow source. The transition is not noise; it is the macro story being rewritten in real time.

The honest framing for readers: the BTC/Gold pair operates as a substitution pair in some historical periods and not in others. Both modes occur. Periods of extended substitution-driven cointegration alternate with periods of complete decoupling, and the alternation itself carries macroeconomic information about which capital allocation regime is currently dominant. The current regime, the rolling p-value, the regime fraction over recent quarters, and the most recent transition date are published continuously at closelook.net/lab/cointegration/. Periodic deep-dive readings of the regime evolution appear in the Quarterly Cointegration Report.

(7) The Second Thesis — BTC and NDX as Lead-Lag Pair

The BTC/NDX pair tests a different hypothesis. Here we are not asking whether BTC and the Nasdaq 100 are cointegrated in a substitutive sense. We are asking whether they share a directional tether — they move in the same direction during On-regimes, but with BTC leading NDX by a measurable lag window.

The intuition: crypto markets trade twenty-four hours a day, seven days a week, including weekends when traditional equity markets are closed. Crypto-native participants build directional positions over weekends in response to overnight news, macro narratives, and sentiment shifts. When traditional equity markets reopen on Monday, institutional risk-on positioning often follows the directional cue established in crypto markets during the closed period. This produces a structural lead-lag where BTC leads NDX by a small but consistent window during On-regimes — typically one to four trading days, with the strongest cross-correlation typically observed in the lag-two-to-three range.

The lead-lag is not a constant, however. During On-regimes, the lag plateau is observable and replicable. During Off-regimes, the lead-lag breaks down — BTC trades on its own halving-cycle dynamics or on idiosyncratic crypto-market news, and NDX trades on equity earnings cycles, Fed expectations, and institutional flows that have no crypto antecedent. When the lead-lag breaks, BTC is no longer a useful early indicator for tech-beta positioning.

The methodological case for this pair is clean for three reasons.

First, the lead-lag has a structural mechanism. The 24/7 vs. 9-to-4 trading-hours asymmetry is a real institutional feature of the market structure, not a statistical artifact. As long as crypto markets remain open during traditional market closures and as long as institutional and retail capital flows remain partially correlated, some version of the lead-lag should persist during On-regimes. This makes the BTC/NDX lead-lag a more durable phenomenon than purely statistical patterns.

Second, the lead-lag drifts within On-regimes in informative ways. When the lead-lag tightens to the lower end of its plateau range — say from a typical two-to-three-day peak down to one-to-two days — the transmission is becoming faster, which usually signals that institutional and crypto-native flows are operating in tighter alignment. When the lead-lag widens to the upper end — three-to-four days — the transmission is slowing, which often precedes a regime break. Watching the drift within the plateau is itself a leading indicator for regime transitions.

Third, the practical applicability is high. Unlike substitution-based pairs where the trading implementation requires shorting one asset against the other, the BTC/NDX lead-lag during On-regimes provides a forward indicator: if BTC moved sharply on the weekend, the directional implication for NDX in the following one-to-four trading days has a measurable historical base rate. This does not constitute a trading recommendation; it constitutes context for decisions made on other grounds. But the context is real and repeatable during On-regimes.

The honest framing for readers: BTC/NDX is cointegrated in some historical periods and not in others. When it is cointegrated, the lead-lag during On-regimes operates in a window of one to four trading days, with the peak typically at lag two to three. The peak migrates within this window as transmission speed varies, and migration toward the upper end of the plateau is an early-warning signal for regime breaks. The current cointegration regime, the rolling p-value, the current peak-lag and plateau bounds, and the lead-lag drift over recent quarters are published continuously at closelook.net/lab/cointegration/. The Quarterly Cointegration Report reviews regime evolution and lead-lag dynamics in depth.

(8) The Joint Reading — A Macro Quadrant Framework

The two pairs, taken individually, each provide a partial reading of the macro environment. Taken together, they provide a much richer reading. The combination of BTC/Gold regime classification and BTC/NDX regime classification produces a 2x2 matrix with four distinct quadrants, each corresponding to a specific macro mode with characteristic implications.

The four quadrants are as follows.

Quadrant One — BTC/Gold Coupled, BTC leads NDX. The Bull Risk-On Mode. Capital is rotating substitutively between Store-of-Value assets, indicating that allocation decisions are being made on relative attractiveness rather than on flight-to-safety urgency. Simultaneously, BTC is leading NDX by a measurable lag, indicating that crypto-native sentiment is feeding institutional risk-on positioning. The macro interpretation: a healthy bull market with cross-asset confirmation. Liquidity is supportive, risk appetite is positive, and the cross-asset transmission mechanisms that characterize mature bull markets are operating normally.

Quadrant Two — BTC/Gold Coupled, BTC does not lead NDX. The Asymmetric Risk Mode. The substitution dynamic between BTC and Gold is operating, suggesting capital is rotating between Store-of-Value assets. But BTC is not providing a forward indicator for NDX, which means the equity market is operating on its own drivers — earnings cycles, sector rotations, Fed policy expectations — independent of crypto sentiment. The macro interpretation: capital is differentiating between asset classes more sharply than usual. This regime often appears in late-cycle markets where institutional positioning has become more disciplined and less correlated with retail-driven crypto flows.

Quadrant Three — BTC/Gold Decoupled, BTC leads NDX. The Crypto-Driven Risk-On Mode. BTC and Gold are not in a substitution relationship — BTC is trading on its own halving-cycle or crypto-native dynamics independent of macro Store-of-Value flows. But BTC is still providing a forward indicator for NDX, which means crypto-driven risk-on sentiment is still flowing into equity positioning even though the broader Store-of-Value substitution mechanic is suspended. The macro interpretation: a risk-on regime driven primarily by crypto-native catalysts (Halving, ETF flows, regulatory clarity) rather than by broad macro liquidity.

Quadrant Four — Both relationships broken. The Structural Stress Mode. Neither the substitution dynamic nor the lead-lag is detectable. BTC is operating on idiosyncratic factors. The Cointegration Monitor cannot tether it to either Gold or NDX. The macro interpretation: structural stress is dominating asset behavior. This regime appears during major crises (FTX collapse in Q4 2022, regional banking stress in early 2023, war-asset dispatch periods). It is the regime where Cointegration provides the least information — but the regime classification itself is the information. Knowing that we are in a structural-stress regime is itself useful, because it tells us that the standard cross-asset reading frameworks are temporarily not applicable and other tools (Volatility regime, Liquidity regime, Sentiment extremes) should take precedence.

The Joint Reading is the methodological summary tool of this Lab Read. It is not a trading signal. It is a Macro-Reading-Tool. It tells us which quadrant the market is currently in, and the quadrant carries an interpretation about what kind of regime we are in and which other analytical frameworks are most likely to be informative. Readers should think of it as one input among several into their own macro thesis-formation process — alongside the Money Temperature reading, the Weekly Signal composite, and the Pattern Engine output.

The current quadrant assignment, the path of recent quadrant transitions, and the macro context for each transition are published continuously at closelook.net/lab/cointegration/ and reviewed in depth in the Quarterly Cointegration Report.

(9) Where Cointegration Fails — An Honest Limitations Section

The methodology described above is real and useful. It is also limited in important ways, and any responsible deployment must understand the limitations before treating the regime classification as actionable.

The first failure mode is structural breaks within rolling windows. The 180-day rolling window assumes that within any 180-day period, the underlying relationship is approximately stable. When a structural break occurs in the middle of a window, the test statistics become contaminated. A break that occurs ninety days before today is partially absorbed by sixty percent of the window, producing an ambiguous reading that is neither truly the old regime nor the new regime. This contamination period typically lasts about ninety trading days after a structural break before the rolling window has fully transitioned to the new regime. Readers should be cautious in interpreting regime classifications during the ninety days following major macro events.

The second failure mode is spurious cointegration in trended pairs. When two assets trend strongly in the same direction over a long period, simple cointegration tests can register a false positive even when no true structural tether exists. Both assets are simply riding the same broad trend, and the spread appears stationary because both legs are growing at similar rates. The Engle-Granger procedure has known weaknesses in this case, and various adjustments — De-Trended Fluctuation Analysis, Phillips-Perron tests with trend correction — exist in the academic literature. The Cointegration Monitor implements a simple correction by including time as a regressor in the spread construction, but this correction is partial. Readers should treat On-regime classifications during periods of strongly trending markets with additional skepticism.

The third failure mode is regime transition lag. The 180-day rolling window is a smoothing filter. It cannot detect a regime transition that occurred yesterday. When the underlying relationship breaks, the rolling test will register the break gradually as the new data accumulates within the window, with full recognition typically requiring approximately ninety trading days. This means the methodology is structurally late at detecting transitions. The Hurst Exponent and Halflife metrics provide some leading information — the Hurst rises and the Halflife extends before the ADF p-value crosses threshold — but the leading-indicator value is partial, not complete. There is no way to detect tomorrow's regime transition in today's data.

The fourth failure mode is the small-sample problem. Eight years of daily data sounds substantial, but many regime durations span twelve to eighteen months. This means that across the full 2018-2026 period, we observe perhaps four to eight distinct regime episodes per pair. Statistical inference based on four to eight observations is intrinsically uncertain, regardless of how clean the methodology is. Claims about "average regime duration" or "fraction of time in On-regime" carry substantial standard errors that grow as the sample shrinks. Readers should treat regime statistics as point estimates with wide confidence intervals, not as precise quantifications.

The fifth failure mode is the joint-reading interpretation risk. The 2x2 Macro-Quadrant framework is a heuristic, not a validated forecasting model. The interpretations attached to each quadrant — Bull Risk-On Mode, Asymmetric Risk Mode, Crypto-Driven Risk-On Mode, Structural Stress Mode — are derived from theoretical reasoning about the macroeconomics of each combination, not from rigorous out-of-sample backtesting of forecast accuracy. The framework provides a useful organizational structure for thinking about cross-asset relationships, but it should not be treated as a deterministic predictor of asset returns. A market in Quadrant One is not guaranteed to behave like other historical Quadrant One periods, particularly when the macro environment differs in structural ways from those historical periods.

The honest summary: the rolling-window cointegration methodology is a meaningful upgrade over single-sample tests and over correlation analysis. It detects real structural tethers when they exist, and it detects regime breaks before correlation-based tools would. It is not a complete macro-reading tool, however. It is one input among several, and its limitations — particularly transition lag, small-sample uncertainty, and structural break contamination — are real constraints on what the methodology can deliver.

(10) Cointegration In The Closelook Stack — And Where To Watch It Live

The Cointegration Monitor is one element of a broader Lab architecture at Closelook. The Lab Reads document the methodology behind each tool; the live tools at closelook.net/lab/ surface the current readings. Cointegration sits alongside Money Temperature (the macro regime monitor) and Lab Grid (the multi-asset Hurst and cointegration scoring across sixty-plus ETFs) as the third foundational quantitative lens on the global tape.

This Lab Read is the methodology. The current values, regime classifications, p-value evolutions, and joint-quadrant assignments live in three complementary surfaces.

For the BTC pairs specifically, the Cointegration Monitor will be expanded with dedicated sub-pages at closelook.net/lab/cointegration/btcgold/ and closelook.net/lab/cointegration/btcndx/. Each sub-page will publish the live regime classification, the rolling p-value time series, the supplementary Hurst and Halflife metrics, and for BTC/NDX the lead-lag plateau range. The pages will update automatically as new daily data arrives.

The Lab Read methodology series will continue with three further pairs of broad macro relevance, each receiving its own Lab Read in this format. SPX vs. global ex-US (the regional dispersion question), Oil vs. USD (the commodity-currency question), and HYG vs. SPX (the credit-equity tether) are the planned next entries. Each will follow the same structural template — two method families, rolling-window methodology, the worked theses, joint readings where applicable, and honest limitations — so that the methodological approach becomes consistent across the Lab Reads library and readers can develop fluency with the framework that transfers across pairs.

The Lab explains the why. The Monitor shows you the now. Together they form the complete loop: a quantitative macro-reading framework with deep methodological foundations, deployed as a live operational tool, published continuously, and explained openly enough that readers can understand exactly what the engine is doing and exactly where it can fail.

(11) Risk Disclosure & Methodology Notes

This Lab Read is a methodological dossier published for educational and research purposes by Closelook. It does not constitute investment advice, a solicitation to buy or sell securities, or a recommendation regarding any specific trading strategy. The Cointegration Monitor generates systematic regime classifications based on the methodology described above; the decision to act on any classification, the position sizing, the risk management, and the portfolio construction context are entirely the responsibility of the reader.

The historical worked theses in this dossier are descriptive characterizations of the methodology applied to specific asset pairs. They are not predictions about future regime durations or transition timing. The cointegration relationships described here have weakened, broken, and re-formed multiple times in the past and will continue to do so in the future. The methodology is designed to detect these transitions, not to prevent them.

The methodology described here, including the 180-day rolling window default, the Engle-Granger ADF p-value thresholds for regime classification, and the Cross-Correlation Function lead-lag computation, reflects the Cointegration Monitor implementation as of publication and may evolve as additional data, additional sensitivity-testing results, and additional academic research are incorporated. All updates to the methodology will be published openly on the Pattern Lab hub.

Closelook publications are intended for sophisticated investors who understand quantitative pattern analysis and can independently assess the limitations of any systematic signal. Readers requiring personalized investment advice should consult a licensed financial advisor.

Closelook — Systematic Market Intelligence for global tech investing

Editor: Thomas Look · Closelook Venture GmbH

A Closelook Lab Read · Published as part of the Pattern Lab methodology series

V3 — methodology-only edition. April 28, 2026. V2's worked-example tables, joint quadrant timeline, and "Now Reading" snapshot box have been removed from this document; current readings now live exclusively at the Cointegration Monitor, the Quarterly Cointegration Report, and the Weekly Signal. The methodology itself remains as documented in V2 with the Halflife refinement to the Ornstein-Uhlenbeck mean-reversion model.