longbridge-quant-stats

name	longbridge-quant-stats
description	Quantitative statistics framework for time-series analysis using Longbridge price data — ADF unit root test (stationarity), cointegration (Engle-Granger / Johansen), GARCH volatility modelling (conditional heteroskedasticity), regression diagnostics (Durbin-Watson / Breusch-Pagan), bootstrap confidence intervals, hypothesis tests (t-test / F-test). Requires statsmodels and scipy. Triggers: "量化统计", "ADF检验", "单位根", "协整检验", "GARCH", "自相关", "异方差", "Bootstrap", "假设检验", "量化統計", "ADF檢驗", "單位根", "協整檢驗", "異方差", "假設檢驗", "quantitative statistics", "ADF test", "unit root", "cointegration", "GARCH", "autocorrelation", "heteroskedasticity", "bootstrap", "hypothesis test", "statsmodels".
license	MIT
metadata	{"author":"longbridge","version":"1.0.0","risk_level":"read_only","requires_login":false,"default_install":true,"requires_mcp":false,"tier":"read"}

longbridge-quant-stats

Apply rigorous statistical methods to financial time-series data retrieved from Longbridge — test assumptions before modelling, diagnose residuals, and produce statistically sound inferences.

Response language: match the user's input language — Simplified Chinese / Traditional Chinese / English.

When to use

• "帮我做 ADF 单位根检验", "run an ADF test on this price series", "幫我做 ADF 單位根檢驗"
• "AAPL 和 MSFT 有没有协整关系", "are AAPL and MSFT cointegrated"
• "用 GARCH 建模波动率", "model volatility with GARCH"
• "回归残差有没有自相关", "check residual autocorrelation (Durbin-Watson)"
• "用 Bootstrap 估计置信区间", "bootstrap confidence interval for Sharpe ratio"

For factor IC/IR testing, use longbridge-factor-research. For pairs-trading cointegration application, use longbridge-pairs-trading.

Prerequisites

pip install statsmodels scipy numpy pandas

Workflow and test catalogue

Step 1 — Fetch price data

longbridge kline --help
longbridge kline <SYMBOL> --period day --count 252 --format json

Extract the close price series. Compute log returns: r_t = ln(P_t / P_{t-1}).

Step 2 — Stationarity: ADF Unit Root Test

When to use: Before regression or time-series modelling — most models require stationary series.

Python (statsmodels):

from statsmodels.tsa.stattools import adfuller
result = adfuller(series, autolag='AIC')
# result: (adf_stat, p_value, lags, n_obs, critical_values, icbest)

Interpretation:

• p < 0.05 → reject unit root → series is stationary.
• p ≥ 0.05 → fail to reject → series has unit root → difference the series.
• Log prices: usually non-stationary. Log returns: usually stationary.

Step 3 — Cointegration Test

When to use: Two non-stationary series may share a long-run equilibrium (pairs trading).

Engle-Granger (two-series):

from statsmodels.tsa.stattools import coint
t_stat, p_value, critical_values = coint(series_A, series_B)
# p < 0.05 → cointegrated

Johansen (multivariate):

from statsmodels.tsa.vector_ar.vecm import coint_johansen
result = coint_johansen(df, det_order=0, k_ar_diff=1)
# trace statistic vs critical values at 90%/95%/99%

Report: test statistic, p-value, critical values, and cointegrating vector.

Step 4 — GARCH Volatility Modelling

When to use: Financial returns show volatility clustering (ARCH effects).

from arch import arch_model
model = arch_model(returns * 100, vol='Garch', p=1, q=1)
res = model.fit(disp='off')
print(res.summary())

Note: pip install arch required in addition to statsmodels.

Output: omega, alpha (ARCH), beta (GARCH) coefficients. Persistence = alpha + beta. If > 0.95, volatility is highly persistent.

ARCH-LM test first (to verify ARCH effects exist):

from statsmodels.stats.diagnostic import het_arch
lm_stat, p_value, f_stat, f_p = het_arch(residuals)

Step 5 — Regression Diagnostics

After running OLS (statsmodels.api.OLS), check:

Test	Purpose	Command
Durbin-Watson	Serial autocorrelation in residuals	statsmodels.stats.stattools.durbin_watson(resid)
Breusch-Pagan	Heteroskedasticity	statsmodels.stats.diagnostic.het_breuschpagan(resid, exog)
Jarque-Bera	Normality of residuals	statsmodels.stats.stattools.jarque_bera(resid)
VIF	Multicollinearity	statsmodels.stats.outliers_influence.variance_inflation_factor

Interpret Durbin-Watson: ~2.0 = no autocorrelation; < 1.5 = positive autocorrelation; > 2.5 = negative autocorrelation.

Step 6 — Bootstrap Confidence Intervals

When to use: Non-normal distributions; small samples; estimating CI for Sharpe ratio, IC, or any statistic.

import numpy as np

def bootstrap_ci(data, stat_fn, n_boot=10000, ci=0.95):
    boots = [stat_fn(np.random.choice(data, len(data), replace=True))
             for _ in range(n_boot)]
    lo = np.percentile(boots, (1 - ci) / 2 * 100)
    hi = np.percentile(boots, (1 + ci) / 2 * 100)
    return lo, hi

# Example: Sharpe ratio CI
sharpe_lo, sharpe_hi = bootstrap_ci(returns, lambda x: x.mean() / x.std() * np.sqrt(252))

Step 7 — Hypothesis Tests

Test	Use case	Function
t-test (one sample)	Is mean IC > 0?	scipy.stats.ttest_1samp(ic_series, 0)
t-test (two sample)	Is long portfolio return > short portfolio?	scipy.stats.ttest_ind(long_ret, short_ret)
F-test / ANOVA	Are returns different across deciles?	scipy.stats.f_oneway(*decile_returns)
Mann-Whitney U	Non-parametric alternative to t-test	scipy.stats.mannwhitneyu(a, b)

Always report: test statistic, p-value, degrees of freedom, and conclusion at 5% significance level.

CLI

longbridge kline --help
longbridge kline <SYMBOL> --period day --count 252 --format json

Output

For each test present:

1. Test name and null hypothesis.
2. Test statistic and p-value.
3. Critical values (where applicable).
4. Conclusion at 5% significance.
5. Practical implication for the user's use case.

Error handling

Situation	简体回复	繁體回覆	English reply
command not found: longbridge	请安装 longbridge-terminal 或检查 MCP 配置。	請安裝 longbridge-terminal 或檢查 MCP 配置。	Install longbridge-terminal or check MCP config.
ModuleNotFoundError: statsmodels	请运行 pip install statsmodels scipy numpy pandas。	請執行 pip install statsmodels scipy numpy pandas。	Run pip install statsmodels scipy numpy pandas.
Insufficient data (< 30 observations)	样本量过小，统计结论可靠性有限，建议延长数据期。	樣本量過小，建議延長數據期。	Sample too small; extend the data period for reliable results.
ARCH module missing for GARCH	请运行 pip install arch 以使用 GARCH 模型。	請執行 pip install arch 以使用 GARCH 模型。	Run pip install arch for GARCH modelling.

Related skills

• longbridge-factor-research — IC/IR factor testing
• longbridge-pairs-trading — cointegration-based pairs trading
• longbridge-correlation — cross-asset correlation analysis
• longbridge-volatility-strategy — volatility modelling and trading

File layout

skills/longbridge-quant-stats/
└── SKILL.md