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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中文题目课程波动率与机制转换模型 · 时间序列分析
ARCH 与 GARCH 模型
某私募(private fund)的风控会上，研究员甩出沪深300 日收益的实证表：日内收益序列本身的自相关系数 公式 在滞后 公式 时几乎全部落在 公式 的 Bartlett 带内；可一旦把同一条序列 平方 再画一次 ACF，从滞后 1 到滞后 60 全是正值、缓慢衰减。再算样本峰度：5.8——远大于正态分布(Gaussian distributi...
打开 →题目3111 · 统计
Does This GARCH Have a Finite Long-Run Variance?
For a GARCH(1,1) model with $\omega=\frac{1}{5}$, $\alpha=\frac{1}{4}$, and $\beta=\frac{3}{4}$, decide whether the model has a finite unconditional variance. If it does, compute it.
打开 →题目6028 · 统计
Fat Tails: Unconditional Kurtosis of GARCH Returns
Let $r_t=\sqrt{h_t}\,z_t$ with $z_t\sim N(0,1)$ i.i.d. and GARCH(1,1) variance. The unconditional kurtosis (when finite) is $K=\dfrac{3\,[1-(\alpha+\beta)^2]}{1-(\alpha+\beta)^2-2\alpha^2}$. For $\alpha=0.1$, $\beta=0.85$, compute $K$ and state whether returns are leptokurtic. Gi
打开 →题目3091 · 统计
Long-Run Variance of a Quiet GARCH Process
For a GARCH(1,1) model $h_t=\omega+\alpha r_{t-1}^2+\beta h_{t-1}$ with $\omega=\frac{1}{10}$, $\alpha=\frac{1}{5}$, and $\beta=\frac{3}{5}$, assume $\alpha+\beta<1$. Compute the unconditional variance $E[h_t]$.
打开 →题目6023 · 统计
Long-Run Volatility (Not Variance) from GARCH Parameters
A GARCH(1,1) model $h_t=\omega+\alpha r_{t-1}^2+\beta h_{t-1}$ has $\omega=0.04$, $\alpha=0.12$, $\beta=0.80$. Here $h_t$ is the conditional variance of daily returns. Report the long-run (unconditional) daily volatility $\sqrt{\bar h}$ as a decimal.
打开 →题目2778 · 脑筋急转弯
Overlapping Search Patterns
A searcher can use one of two search patterns: Pattern 1 checks locations $A$ and $B$, while Pattern 2 checks locations $B$ and $C$. The hider chooses one location. Row's payoff is $1$ if the chosen pattern covers the hider's location and $0$ otherwise. Find the equilibrium and t
打开 →题目4382 · 机器学习
Search Space Width
The best score in your search occurs at the largest regularization value on the grid. What does that suggest as the next tuning step?
打开 →题目2771 · 脑筋急转弯
Searching Boxes With Unequal Stakes
A searcher chooses one of three boxes to inspect; a hider chooses one box to hide in. If the searcher picks the correct box, the searcher earns the box's value; otherwise the payoff is $0$. The three box values are $6$, $3$, and $2$. Find the searcher's optimal mixed strategy and
打开 →题目3093 · 统计
Steady Variance from Daily GARCH Parameters
For a GARCH(1,1) model $h_t=\omega+\alpha r_{t-1}^2+\beta h_{t-1}$ with $\omega=1$, $\alpha=\frac{1}{10}$, and $\beta=\frac{4}{5}$, assume $\alpha+\beta<1$. Compute the unconditional variance $E[h_t]$.
打开 →题目6027 · 统计
When GARCH(1,1) Becomes EWMA
RiskMetrics EWMA updates variance as $h_t=(1-\lambda)r_{t-1}^2+\lambda h_{t-1}$. State the constraints on $(\omega,\alpha,\beta)$ that make GARCH(1,1) coincide exactly with EWMA, and give the implied $\lambda$ when $\alpha=0.06$. Report $\lambda$ as a decimal.
打开 →题目4339 · 机器学习
Why Architecture Mismatch Hurts
Why can architecture mismatch dominate parameter count when performance is poor?
打开 →课程波动率与机制转换模型 · 时间序列分析
非对称与多元 GARCH
周五下午两点,沪深300 当日累计跌幅已经放大到 2.8%、还在加速。你在一家中型私募(private fund)做日内风险报表,上周用对称 GARCH(1, 1) 给组合估的次日条件方差,在过去三次类似的放量下跌之后,滚动校准里都低估了实际 realised vol 将近 30%——而向上的同尺度日子,模型反而略偏高。问题不在样本,也不在 公式 是否服从正...
打开 →题目4289 · 机器学习
Why Hierarchical Clustering Can Be Useful
Why can clustering raw price levels of stocks be misleading compared with clustering normalized returns or features?
打开 →课程波动率 · 衍生品
已实现波动率、GARCH 与 VIX
周三下午 15:05，SSE 主板刚收盘。某 私募 vol 套利团队的基金经理在 T+1 结算窗口前打开两个数字。第一是当天早盘 中金所 公布的 iVX 读数：18.3。第二是 沪深300 指数过去 30 个交易日的已实现波动率，按收盘到收盘对数收益率的年化标准差算：13.8。这 4.5 个 vol 点的缺口——隐含波动率（implied volatilit...
打开 →题目4390 · 机器学习
Before Blaming The Search
The current best setting sits at extreme values on both the learning-rate and regularization grids. What should your next search action be?
打开 →题目3224 · 统计
Hierarchical Bayes Versus Bonferroni
You are screening 200 alphas and most are probably zero. Why does hierarchical Bayes approach this problem differently from Bonferroni-style frequentist correction?
打开 →题目2455 · 机器学习
Repeated Validation Peeking During Research
A researcher keeps trying new transformations and only retains the ones that improve the same validation score. Why does the validation set stop being a clean model-selection tool?
打开 →题目2701 · 机器学习
Search Depth Hidden in Design Knobs
A team tried 4 universes, 5 rebalance frequencies, and 6 transaction-cost assumptions before reporting the best result. How many distinct design combinations were implicitly searched?
打开 →题目1699 · 统计
Sidak Cutoff for 18 Effective Research Choices
A desk believes its many correlated parameter tweaks boil down to 18 effectively independent research choices. What Sidak per-choice cutoff controls family-wise error at 5%?
打开 →题目365 · 概率
Three-Level Normal Hierarchy: Iterated Tower and Smoothing
Consider a three-level normal hierarchy: $Z \sim N(0, 1)$, then $Y \mid Z \sim N(Z, 1)$, then $X \mid Y \sim N(Y, 1)$. (a) Using iterated expectations, find $E[X]$ and $\operatorname{Var}(X)$. (b) Find $E[X \mid Z]$ by applying the tower property: $E[X \mid Z] = E[E[X \mid Y] \
打开 →题目1707 · 统计
Why Hierarchical Testing Can Help
A researcher first tests whether a sector shows any effect, and only if that passes does she test stocks inside that sector. Why can this hierarchical design reduce the multiplicity burden?
打开 →题目2714 · 机器学习
Why Search Depth Is Bigger Than the Number of Named Strategies
Why can a team that claims to have tested only five named strategies still have conducted a much deeper search than that number suggests?
打开 →题目2708 · 机器学习
Why Universe Choice Is Part of the Search Tree
Why should changing the tradable universe be counted as another research branch rather than as harmless context?
打开 →题目2696 · 机器学习
False Strategy Surviving Two Independent Research Gates
A desk tries 80 genuinely null strategy ideas. A strategy is kept only if it passes an in-sample screen at 10% and then a fresh out-of-sample confirmation at 5%, with the two tests treated as independent under the null. What is the probability at least one null idea survives both
打开 →题目4377 · 机器学习
Grid Or Random Search
A feature standardization step is fitted on the full dataset before cross-validation instead of inside each fold. What is the main tuning problem with that workflow?
打开 →题目1704 · 统计
In-Sample Screen Needed After a 10-Lag Search
A desk tries 10 lags for a genuinely null signal, keeps the best in-sample lag if any lag has p-value below alpha, and then requires a fresh holdout p-value below 10%. What alpha makes the overall false-launch probability exactly 2%, assuming independence under the null?
打开 →题目2646 · 机器学习
Model-Fit Count in a Nested CV Search
A team runs 5 outer folds. Inside each outer-training split, it evaluates 6 hyperparameter settings by 4-fold CV, then refits the chosen model once on the full outer-training split. How many total model fits are performed?
打开 →题目2788 · 脑筋急转弯
Search Three Targets With Values 5, 3, and 2
A defender can inspect exactly one of three targets. If the attacker chooses the inspected target, the defender earns the target's value; otherwise the defender gets $0$. The target values are $5$, $3$, and $2$. Find the defender's optimal inspection mix and the value.
打开 →题目2519 · 机器学习
Why Hyperparameter Search Belongs Outside the Test Set 24
Why is tuning lambda on the test set just as problematic here as in any other ML pipeline?
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