longbridge-quant-stats

Original：🇺🇸 English

Translated

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".

2installs

Sourcelongbridge/skills

Added on2026-05-13

NPX Install

npx skill4agent add longbridge/skills longbridge-quant-stats

SKILL.md Content

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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

bash

pip install statsmodels scipy numpy pandas

Workflow and test catalogue

Step 1 — Fetch price data

bash

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):

python

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):

python

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

Johansen (multivariate):

python

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).

python

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):

python

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.

python

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

bash

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

Output

For each test present:

Test name and null hypothesis.
Test statistic and p-value.
Critical values (where applicable).
Conclusion at 5% significance.
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

longbridge-quant-stats

NPX Install

Tags

SKILL.md Content

longbridge-quant-stats

When to use

Prerequisites

Workflow and test catalogue

Step 1 — Fetch price data

Step 2 — Stationarity: ADF Unit Root Test

Step 3 — Cointegration Test

Step 4 — GARCH Volatility Modelling

Step 5 — Regression Diagnostics

Step 6 — Bootstrap Confidence Intervals

Step 7 — Hypothesis Tests

CLI

Output

Error handling

Related skills

File layout