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 →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 →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?
打开 →题目2712 · 机器学习
Why Many Small Tweaks Still Count as Deep Search
Why is it misleading to claim that no serious overfitting occurred just because the final strategy differs from the baseline by only many small tweaks?
打开 →题目4334 · 机器学习
Before Using CNN
What is the first structural property you should verify before leaning on a CNN as your main architecture?
打开 →题目4327 · 机器学习
CNN Depth For Longer Horizon
A stride-1 CNN uses kernel size 3 and no dilation. To cover a dependency horizon of 9 steps you need 4 layers. If the required horizon rises to 41 steps, how many layers are needed, and what does that imply about the architecture pressure?
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