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longbridge-quant-stats

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Original

English
🇨🇳

Translation

Chinese

longbridge-quant-stats

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.
对从Longbridge获取的金融时间序列数据应用严谨的统计方法——在建模前检验假设、诊断残差，并生成统计可靠的推断结果。
响应语言：匹配用户输入语言——简体中文 / 繁体中文 / 英文。

When to use

使用场景

  • "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
.
  • "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"
若需进行因子IC/IR检验，请使用
longbridge-factor-research
。若需基于协整的配对交易应用，请使用
longbridge-pairs-trading
。

Prerequisites

前置依赖

bash
pip install statsmodels scipy numpy pandas
bash
pip install statsmodels scipy numpy pandas

Workflow and test catalogue

工作流程与测试目录

Step 1 — Fetch price data

步骤1 — 获取价格数据

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})
.
bash
longbridge kline --help
longbridge kline <SYMBOL> --period day --count 252 --format json
提取
close
收盘价序列。计算对数收益率：
r_t = ln(P_t / P_{t-1})
。

Step 2 — Stationarity: ADF Unit Root Test

步骤2 — 平稳性检验：ADF单位根检验

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')
适用场景：在回归或时间序列建模前——大多数模型要求序列具备平稳性。
Python（statsmodels库）:
python
from statsmodels.tsa.stattools import adfuller
result = adfuller(series, autolag='AIC')

result: (adf_stat, p_value, lags, n_obs, critical_values, icbest)

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.

**结果解读**:
- p < 0.05 → 拒绝单位根假设 → 序列平稳。
- p ≥ 0.05 → 无法拒绝假设 → 序列存在单位根 → 需对序列进行差分处理。
- 对数价格：通常非平稳。对数收益率：通常平稳。

Step 3 — Cointegration Test

步骤3 — 协整检验

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)
适用场景：两个非平稳序列可能存在长期均衡关系（配对交易场景）。
Engle-Granger法（双序列）:
python
from statsmodels.tsa.stattools import coint
t_stat, p_value, critical_values = coint(series_A, series_B)

p < 0.05 → cointegrated

p < 0.05 → 存在协整关系


**Johansen (multivariate)**:
```python
from statsmodels.tsa.vector_ar.vecm import coint_johansen
result = coint_johansen(df, det_order=0, k_ar_diff=1)

**Johansen法（多变量）**:
```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%

迹统计量与90%/95%/99%置信水平下的临界值对比


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

输出内容：检验统计量、p值、临界值以及协整向量。

Step 4 — GARCH Volatility Modelling

步骤4 — GARCH波动率建模

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)
适用场景：金融收益率存在波动率聚类（ARCH效应）时。
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())
注意：除statsmodels外，还需执行
pip install arch
安装依赖库。
输出：omega、alpha（ARCH项）、beta（GARCH项）系数。持续性 = alpha + beta。若该值>0.95，说明波动率具备高度持续性。
先进行ARCH-LM检验（验证是否存在ARCH效应）:
python
from statsmodels.stats.diagnostic import het_arch
lm_stat, p_value, f_stat, f_p = het_arch(residuals)

Step 5 — Regression Diagnostics

步骤5 — 回归诊断

After running OLS (
statsmodels.api.OLS
), check:
TestPurposeCommand
Durbin-WatsonSerial autocorrelation in residuals
statsmodels.stats.stattools.durbin_watson(resid)
Breusch-PaganHeteroskedasticity
statsmodels.stats.diagnostic.het_breuschpagan(resid, exog)
Jarque-BeraNormality of residuals
statsmodels.stats.stattools.jarque_bera(resid)
VIFMulticollinearity
statsmodels.stats.outliers_influence.variance_inflation_factor
Interpret Durbin-Watson: ~2.0 = no autocorrelation; < 1.5 = positive autocorrelation; > 2.5 = negative autocorrelation.
运行OLS回归（
statsmodels.api.OLS
）后，需检查以下内容：
检验方法用途命令
Durbin-Watson检验残差的序列自相关性
statsmodels.stats.stattools.durbin_watson(resid)
Breusch-Pagan检验异方差性
statsmodels.stats.diagnostic.het_breuschpagan(resid, exog)
Jarque-Bera检验残差的正态性
statsmodels.stats.stattools.jarque_bera(resid)
VIF检验多重共线性
statsmodels.stats.outliers_influence.variance_inflation_factor
Durbin-Watson结果解读：~2.0 = 无自相关性；<1.5 = 正自相关性；>2.5 = 负自相关性。

Step 6 — Bootstrap Confidence Intervals

步骤6 — Bootstrap置信区间估计

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
适用场景：数据分布非正态、样本量较小、估计夏普比率/IC或其他统计量的置信区间时。
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

示例：夏普比率置信区间

sharpe_lo, sharpe_hi = bootstrap_ci(returns, lambda x: x.mean() / x.std() * np.sqrt(252))
undefined
sharpe_lo, sharpe_hi = bootstrap_ci(returns, lambda x: x.mean() / x.std() * np.sqrt(252))
undefined

Step 7 — Hypothesis Tests

步骤7 — 假设检验

TestUse caseFunction
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 / ANOVAAre returns different across deciles?
scipy.stats.f_oneway(*decile_returns)
Mann-Whitney UNon-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.
检验方法适用场景函数
单样本t检验因子IC均值是否>0？
scipy.stats.ttest_1samp(ic_series, 0)
双样本t检验多头组合收益率是否>空头组合？
scipy.stats.ttest_ind(long_ret, short_ret)
F检验/方差分析不同分位数组合的收益率是否存在差异？
scipy.stats.f_oneway(*decile_returns)
Mann-Whitney U检验t检验的非参数替代方法
scipy.stats.mannwhitneyu(a, b)
需始终报告：检验统计量、p值、自由度，以及在5%显著性水平下的结论。

CLI

命令行工具（CLI）

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

Output

输出内容

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.
对于每个执行的检验：
  1. 检验名称与原假设。
  2. 检验统计量与p值。
  3. 临界值（如适用）。
  4. 在5%显著性水平下的结论。
  5. 对用户实际场景的实用建议。

Error handling

错误处理

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.
场景简体回复繁体回覆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
.
数据不足（<30个观测值）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.
GARCH所需ARCH模块缺失请运行 
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

相关技能

  • 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
  • longbridge-factor-research
    — 因子IC/IR检验
  • longbridge-pairs-trading
    — 基于协整的配对交易
  • longbridge-correlation
    — 跨资产相关性分析
  • longbridge-volatility-strategy
    — 波动率建模与交易

File layout

文件结构

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