cointegration-analysis Checked

• Based on a VAR model: ΔY_t = Π·Y_{t-1} + Σ Γ_i·ΔY_{t-i} + ε_t
• Tests the rank of the Π matrix
• Uses trace test and maximum eigenvalue test
• Returns: number of cointegrating vectors and the vectors themselves

from statsmodels.tsa.vector_ar.vecm import coint_johansen

# data: T×N array of price series
result = coint_johansen(data, det_order=0, k_ar_diff=1)

# Trace statistic vs critical values (90%, 95%, 99%)
trace_stats = result.lr1          # Trace statistics
trace_crit = result.cvt           # Critical values
max_eigen_stats = result.lr2      # Max eigenvalue statistics
max_eigen_crit = result.cvm       # Critical values

# Cointegrating vectors
coint_vectors = result.evec

### 3. Phillips-Ouliaris

Similar to Engle-Granger but uses Phillips-Perron style test statistics

instead of ADF. More robust to heteroskedasticity and serial correlation in

the residuals. Available via statsmodels.tsa.stattools.coint.

from statsmodels.tsa.stattools import coint

# Returns: test statistic, p-value, critical values
t_stat, p_value, crit_values = coint(y_prices, x_prices)
cointegrated = p_value < 0.05

Practical Workflow

### Step 1: Screen Pairs by Correlation

Pre-filter using Pearson correlation > 0.7 to reduce the number of

cointegration tests (which are more expensive).

### Step 2: Test Cointegration

Run Engle-Granger in both directions. Use p < 0.05 threshold.

### Step 3: Estimate Hedge Ratio

Use OLS for simplicity. For production, consider Total Least Squares or

Dynamic OLS (see references/methodology.md).

### Step 4: Compute Spread

spread = y_prices - hedge_ratio * x_prices - intercept
z_score = (spread - spread.mean()) / spread.std()

### Step 5: Test Spread for Mean Reversion

• **ADF test**: p < 0.05 confirms stationarity
• **Hurst exponent**: H < 0.5 indicates mean reversion (H ≈ 0.5 = random walk)
• **Half-life**: λ from AR(1) on spread; half-life = -ln(2)/ln(λ)
• Viable pairs: half-life between 5 and 60 days

### Step 6: Trade the Spread

If the spread is mean-reverting, it is a viable pairs trade candidate.

See references/pairs_trading.md for entry/exit rules and risk management.

Rolling Cointegration

Cointegration relationships can break down over time due to structural changes,

regime shifts, or evolving market dynamics.

### Rolling Window Approach

Test cointegration on rolling 60–90 day windows:

window = 60
rolling_pvalues = []
rolling_hedges = []

for i in range(window, len(prices)):
    y_win = y_prices[i - window:i]
    x_win = x_prices[i - window:i]
    _, p_val, _ = coint(y_win, x_win)
    slope, intercept, _, _, _ = stats.linregress(x_win, y_win)
    rolling_pvalues.append(p_val)
    rolling_hedges.append(slope)

### Monitoring Signals

| Signal | Healthy | Warning | Stop Trading |

|---|---|---|---|

| Rolling p-value | < 0.05 | 0.05–0.10 | > 0.10 |

| Hedge ratio drift | < 10% change | 10–25% change | > 25% change |

| Spread half-life | 5–60 days | 60–120 days | > 120 days or < 5 |

Crypto Pairs Candidates

### Layer-1 Correlation

• SOL vs ETH — L1 sector beta, often cointegrated during trending markets
• SOL vs AVAX — alternative L1 correlation

### Stablecoins

• USDC vs USDT — should be perfectly cointegrated (peg arbitrage)
• Useful as a sanity check for your cointegration pipeline

### Liquid Staking Derivatives

• mSOL vs jitoSOL — both track SOL staking yield
• stSOL vs mSOL — Lido vs Marinade staking

### Same-Sector Tokens

• DEX tokens: RAY vs ORCA
• Lending tokens: cross-protocol comparison
• Meme tokens: rarely cointegrated, high risk

Common Pitfalls

1. **Spurious cointegration** — Two trending series (both up in a bull market) may

appear cointegrated. Always test on sufficient data (>200 observations) and

check out-of-sample stability.

2. **Structural breaks** — A fundamental change (protocol upgrade, tokenomics

change) can permanently break cointegration. Monitor rolling p-values.

3. **Look-ahead bias** — Estimating the hedge ratio on the full sample and then

backtesting on the same sample inflates results. Always use walk-forward

estimation.

4. **Too-short sample** — Cointegration tests need >100 observations minimum,

ideally >200, to have reasonable power.

5. **Ignoring transaction costs** — Pairs trades involve 4 transactions per

round trip. At 0.3% per leg, that is 1.2% in costs that the spread must

overcome.

6. **Asymmetric cointegration** — The relationship may only hold in one

direction or one regime. Consider threshold cointegration models for

production use.

Integration with Other Skills

• **correlation-analysis** — Pre-screening pairs by correlation before cointegration testing
• **mean-reversion** — Trading the cointegrated spread using mean-reversion entry/exit rules
• **vectorbt** — Backtesting pairs strategies with walk-forward validation
• **regime-detection** — Identifying when cointegration regimes shift
• **volatility-modeling** — Spread volatility forecasting for dynamic position sizing

Files

### References

• references/methodology.md — Engle-Granger details, Johansen derivation, hedge ratio estimation methods, spread construction
• references/pairs_trading.md — En