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中文题目
课程SciPy 与统计工具 · Python 数据与量化分析

scipy.stats 分布对象与描述性统计

周一上午十点，你坐在一家中型私募的研究台。3.2.2 收尾那张 tear sheet 昨晚跑完了，落到磁盘的中间产物里有一行 returns = (closes['510300.SH'].pct change().dropna()).to numpy() ——一根长度 252 的 np.ndarray ，是沪深300 ETF（510300.SH）在 2024...

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模块3.2.3 · 编程 · Python 数据与量化分析

SciPy 与统计工具

python · scipy · stats · distributions · fit · var · descriptive-statistics · hypothesis-testing

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课程SciPy 与统计工具 · Python 数据与量化分析

用 SciPy 做假设检验与置信区间

周五下午两点半，浦东陆家嘴一家中型私募的风控会上，PM 把昨晚跑出来的 tear sheet 推过来：「食品饮料这只 600519.SH 的 63 日滚动 ​夏普比率​ ​（Sharpe ratio）样本期均值是 0.86，银行那两只 000001.SZ 和 600036.SH 是 0.42。0.44 的差，可信吗？」你脑子里第一反应是 3.2.2 L5 那...

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课程SciPy 与统计工具 · Python 数据与量化分析

用 SciPy 做回归与曲线拟合

周三午后，浦东陆家嘴一家中型私募的研究台上，PM 把一张 252 天的样本期跑出来推过来：「 600519.SH 对沪深300 ETF（ 510300.SH ）的 beta 我刚才用 np.linalg.lstsq 解出来是 0.91——但 0.91 离 1 到底有多远？是抽样噪音里飘出来的一格，还是这只票就比沪深300 系统性低 beta？」3.2.1 L...

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课程SciPy 与统计工具 · Python 数据与量化分析

面向 quant 的 scipy.optimize 与 scipy.linalg

周一上午十点，浦东一家中型私募的研究台。PM 把 3.2.2 L5 那张已经稳定跑通的 tear sheet 推过来，篮子是 、252 个交易日的 NumPy 收益矩阵 returns ，形状 公式。「我现在不要单只票的 alpha 也不要 Sharpe——给我四个数：第一，这只 3 票篮子的​ ​最小方差​ ​长仓权重；第二，顶端主成分占多少方差，看篮子风...

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题目1719 · 统计

0.049 vs 0.051 Decision Cliff

Two backtests differ only slightly: one reports p = 0.049 and the other p = 0.051. Why is it bad practice to call one ‘real’ and the other ‘not real’ purely because one is below 0.05?

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题目3221 · 统计

A Confidence Interval Cannot Price a One-Off Launch Decision

A PM sees a frequentist 95% confidence interval for next-month strategy edge of [-0.1, 0.4] and asks, "So what is the probability the true edge is positive for this launch decision?" Why can't the interval answer that question by itself, and what Bayesian quantity would answer it

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题目1653 · 统计

A Smoothed Bernoulli Estimator vs the Sample Proportion

Let $X\sim \mathrm{Binomial}(10,p)$ and consider the estimator $$\delta = \frac{X+1}{12}$$ for $p$. At the parameter value $p=0.2$, compute the bias, variance, and MSE of $\delta$, and compare its MSE with the usual sample proportion $\hat p = X/10$.

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题目1762 · 统计

A Tiny First Stage Is a Weak-Instrument Warning

Two candidate rollouts have the same reduced-form impact on PnL: $$E[Y\mid Z=1]-E[Y\mid Z=0]=0.02.$$ For rollout A, the first stage is $0.20$; for rollout B, the first stage is $0.01$. Which rollout creates the weaker IV design, and why?

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题目3162 · 统计

Allocate Capital Only Above a 60% Posterior

A latent profitable regime has prior probability $\frac{2}{5}$. Independent signals arrive sequentially; each `H` doubles the odds of the regime and each `T` halves them. After the signal string `HHT`, should you act if the required posterior threshold is $\frac{3}{5}$? Also repo

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题目1697 · 统计

Any False Sector Winner After Within-Sector Mining

A desk has 12 sectors, each containing 5 genuinely null variants. In each sector it keeps only the smallest p-value, and it flags the sector if that winning p-value is below 1%. Assuming independence, what is the probability at least one sector is falsely flagged?

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题目1821 · 统计

AR(1) Multi-Step Forecast 1

A signal follows X_t = 0 + 0.6 X_(t-1) + e_t with Var(e_t) = 2 and current value X_t = 10. What is the h = 3 step forecast E[X_(t+3) | X_t]?

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题目1822 · 统计

AR(1) Multi-Step Forecast 2

A signal follows X_t = 4 + 0.7 X_(t-1) + e_t with Var(e_t) = 1.5 and current value X_t = 8. What is the h = 2 step forecast E[X_(t+2) | X_t]?

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题目1823 · 统计

AR(1) Multi-Step Forecast 3

A signal follows X_t = -1 + 0.8 X_(t-1) + e_t with Var(e_t) = 1 and current value X_t = 3. What is the h = 4 step forecast E[X_(t+4) | X_t]?

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题目6026 · 统计

ARCH(1) as the Beta-Zero Special Case

A GARCH(1,1) reduces to ARCH(1) when $\beta=0$: $h_t=\omega+\alpha r_{t-1}^2$. With $\omega=0.7$ and $\alpha=0.3$, compute the unconditional variance $\bar h$ as a decimal.

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题目1883 · 统计

Average Gross Leverage at Launch

A live manager panel shows 27 low-leverage funds and 18 high-leverage funds. Survival rates for those groups were 90% and 60%, respectively. Suppose low-leverage funds average 1.2x gross leverage and high-leverage funds average 2.4x gross leverage. What was the average gross lev

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题目1759 · 统计

Averaging Two Noisy Measurements

Again the structural model is $Y=2X+u$ with $E[u\mid X]=0$, but now you observe two noisy proxies: $$W_1=X+\eta_1, \qquad W_2=X+\eta_2,$$ where $\eta_1,\eta_2$ are independent of each other and of $X,u$. Suppose $\operatorname{Var}(X)=4$ and each noise term has variance 1. If yo

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题目1756 · 统计

Backing Out Omitted Covariance From a Slope Drop

A desk regresses slippage Y on inventory pressure X. Without an urgency control, the OLS slope on X is 0.90. After adding a perfect measure of urgency U, the slope falls to 0.60. Suppose the structural model is Y = beta X + 0.5 U + noise and Var(X)=1. What is Cov(X,U)?

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