第 17 / 17 页
非代码面试题
显示 20 / 340 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
6020Predictive Chance the Next Trade FailsA fill probability p has prior Beta (2,1). After observing 3 fills and 4 misses, what is the posterior predictive probability that the very next attempt is a miss (a failure)?统计中等derivation未尝试免费6022MAP Estimate Versus Posterior MeanAfter updating, the posterior for a conversion rate p is Beta (8,4). Report both the MAP (posterior mode) estimate and the posterior mean, and state which is larger.统计中等derivation未尝试免费6023Long-Run Volatility (Not Variance) from GARCH ParametersA GARCH(1,1) model h t=\omega+ r t-1 2+ h t-1 has \omega=0.04, =0.12, =0.80. Here h t is the conditional variance of daily returns. Report the long-run (unconditional) daily volatility h as a decimal.统计中等derivation未尝试面试订阅6024Persistence and the Covariance-Stationarity VerdictA GARCH(1,1) has =0.20, =0.75. Compute the persistence + and state whether the process is covariance-stationary (i.e. has a finite, time-invariant unconditional variance). Give the persistence as a decimal.统计简单derivation未尝试面试订阅6025Five-Step Forecast via the Mean-Reversion FormulaFor a GARCH(1,1) with \omega=0.2, =0.1, =0.8, the one-step-ahead conditional variance is h t+1 =3. Using the closed form E t[h t+k ]= h+( + ) \,k-1 (h t+1 - h), compute the 5-step-ahead forecast E t[h t+5 ] as a decimal.统计困难derivation未尝试面试订阅6026ARCH(1) as the Beta-Zero Special CaseA GARCH(1,1) reduces to ARCH(1) when =0: h t=\omega+ r t-1 2. With \omega=0.7 and =0.3, compute the unconditional variance h as a decimal.统计简单derivation未尝试面试订阅6027When GARCH(1,1) Becomes EWMARiskMetrics EWMA updates variance as h t=(1- )r t-1 2+ h t-1 . State the constraints on (\omega, , ) that make GARCH(1,1) coincide exactly with EWMA, and give the implied when =0.06. Report as a decimal.统计中等数值题未尝试面试订阅6028Fat Tails: Unconditional Kurtosis of GARCH ReturnsLet r t= 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-( + ) 2] 1-( + ) 2-2 2 . For =0.1, =0.85, compute K and state whether returns are leptokurtic. Give K as a decimal.统计困难derivation未尝试面试订阅6029News-Impact Update from a Signed ReturnA GARCH(1,1) has \omega=0.00001, =0.08, =0.90. Today's conditional variance is h t=0.0004 and today's return is r t=-0.03. Compute tomorrow's conditional variance h t+1 as a decimal.统计中等derivation未尝试面试订阅6030One-Step Prediction with a Persistence CoefficientA latent state evolves as x t=0.9\,x t-1 +w t with w t\sim N(0,2). At time t-1 the filtered state is N(4,3). Compute the one-step-ahead predicted mean and predicted variance of x t (before any observation at time t).统计简单derivation未尝试免费6031Kalman Gain AloneIn a scalar measurement update y=x+\varepsilon with \varepsilon\sim N(0,4), the prior (predicted) state variance is P -=12. What fraction of the innovation is incorporated into the updated estimate, i.e. compute the Kalman gain K.统计简单数值题未尝试免费6032How Much Does One Print Shrink Uncertainty?A predicted state has variance P -=10. A single observation arrives with noise variance R=6 in the model y=x+\varepsilon. By how much does the posterior (updated) variance fall below P -? Give the updated variance P +.统计简单数值题未尝试免费6033Innovation Variance and a Standardized SurpriseIn the model y t=x t+v t with v t\sim N(0,3), the predicted state at time t is N(5,7). You then observe y t=11. Compute the innovation (one-step forecast error) variance S, and the standardized innovation (y t-m -)/ S .统计中等derivation未尝试面试订阅6034Where Does the Estimate Land After the Print?The predicted state is N(8,6) and you observe y=14 with measurement noise variance R=2 in y=x+\varepsilon. Compute only the updated (posterior) mean of the state.统计简单数值题未尝试免费6035Half-Life of a Mean-Reverting SpreadA residual spread follows X (t+1) = 0.8 X t + epsilon (t+1) with zero-mean shocks. In trading days, what is the half-life of mean reversion, i.e. the horizon h at which the expected residual has decayed to half its current value?统计简单数值题未尝试免费6036Implied AR(1) Coefficient From a Target Half-LifeA desk wants a mean-reverting signal whose shocks lose half their expected size every 5 trading days. If the signal is modeled as AR(1), X (t+1) = phi X t + epsilon (t+1), what value of phi is implied?统计中等数值题未尝试面试订阅6037Random-Walk Risk Scaling Over a HorizonA price follows a driftless random walk whose daily increments are iid with standard deviation 2 bp. By what multiple does the standard deviation of the cumulative move grow when the horizon increases from 1 day to 9 days?统计简单数值题未尝试免费6038Sign and Size of Lag-1 AutocorrelationA stationary spread obeys X (t+1) = -0.4 X t + epsilon (t+1) with iid zero-mean shocks. What is the lag-1 autocorrelation of X t, and what does its sign say about period-to-period dynamics?统计中等数值题未尝试面试订阅6039Ornstein-Uhlenbeck Speed to Discrete CoefficientA spread is modeled in continuous time as a mean-reverting Ornstein-Uhlenbeck process with reversion speed kappa = 0.5 per day. If you sample it once per day and fit an AR(1), what discrete coefficient phi should you expect?统计中等数值题未尝试面试订阅6040Two-Period Variance Ratio of an AR(1)Returns are generated by a stationary AR(1) with autoregressive coefficient 0.5. The Lo-MacKinlay variance ratio at lag 2 is VR(2) = Var(r t + r (t+1)) / (2 Var(r t)). Compute VR(2) and state whether it signals momentum or mean reversion.统计困难数值题未尝试面试订阅