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1867RW Versus MR Diagnosis 2After a 10 bp shock, the expected residual is only 2 bp four days later. Does that behavior point more toward random walk or mean reversion?统计简单数值题未尝试免费1868RW Versus MR Diagnosis 3A five-day variance ratio comes in well below 1. What does that suggest about serial dependence in returns?统计中等essay未尝试面试订阅1869RW Versus MR Diagnosis 4If a spread's conditional mean always equals today's level, regardless of horizon, which model is the closer description?统计中等derivation未尝试面试订阅1870RW Versus MR Diagnosis 5A desk notices that expected residual carry from holding a spread for longer horizons quickly saturates instead of growing linearly forever. Is that more consistent with random walk or mean reversion?统计困难derivation未尝试面试订阅3066Signal Extraction from One Noisy PrintA latent scalar state has prior x\sim N(10,4). You observe y=13 through y=x+\varepsilon with \varepsilon\sim N(0,5). Compute the Kalman gain, posterior mean, and posterior variance.统计中等derivation未尝试面试订阅3068Latent Fair-Value UpdateA latent scalar state has prior x\sim N(-1,16). You observe y=3 through y=x+\varepsilon with \varepsilon\sim N(0,9). Compute the Kalman gain, posterior mean, and posterior variance.统计中等derivation未尝试面试订阅3071Local-Level Forecast Then UpdateSuppose x t=x t-1 +w t with w t\sim N(0,2), and y t=x t+v t with v t\sim N(0,3). At time t-1 the filtered state is N(7,4). You observe y t=9. Compute the predicted mean/variance and the updated mean/variance at time t.统计中等derivation未尝试面试订阅3072Random-Walk Value Filter StepSuppose x t=x t-1 +w t with w t\sim N(0,1), and y t=x t+v t with v t\sim N(0,4). At time t-1 the filtered state is N(-2,5). You observe y t=0. Compute the predicted mean/variance and the updated mean/variance at time t.统计中等derivation未尝试面试订阅3076Fusing Two Noisy Dealer QuotesA latent scalar state has prior N(0,9). Two conditionally independent sensors observe y 1=2 with noise variance 4 and y 2=-1 with noise variance 5. Compute the posterior mean and posterior variance after both observations.统计中等derivation未尝试面试订阅3077Two-Sensor Latent Level EstimateA latent scalar state has prior N(5,16). Two conditionally independent sensors observe y 1=9 with noise variance 9 and y 2=3 with noise variance 4. Compute the posterior mean and posterior variance after both observations.统计中等derivation未尝试面试订阅3078Dual Feed State CombinationA latent scalar state has prior N(-2,25). Two conditionally independent sensors observe y 1=-1 with noise variance 1 and y 2=2 with noise variance 4. Compute the posterior mean and posterior variance after both observations.统计中等derivation未尝试面试订阅3081Two Missing Days Before a Print ArrivesA local-level model satisfies x t=x t-1 +w t with w t\sim N(0,1), and observations have noise variance 2. After the last filtered state N(3,4), there are 2 consecutive missing observations. Then you observe a new value y=6. Compute the variance just before the new observation and the updated mean/variance after processing it.统计中等derivation未尝试面试订阅3082One Missing Observation Then UpdateA local-level model satisfies x t=x t-1 +w t with w t\sim N(0,3), and observations have noise variance 5. After the last filtered state N(-1,9), there are 1 consecutive missing observations. Then you observe a new value y=2. Compute the variance just before the new observation and the updated mean/variance after processing it.统计中等derivation未尝试面试订阅3086Steady-State Gain with Q=1, R=2Consider the scalar local-level model in steady state: x t=x t-1 +w t, w t\sim N(0,1), and y t=x t+v t, v t\sim N(0,2). Compute the steady-state posterior variance C and the steady-state Kalman gain K.统计困难derivation未尝试面试订阅3091Long-Run Variance of a Quiet GARCH ProcessFor a GARCH(1,1) model h t=\omega+ r t-1 2+ h t-1 with \omega= 1 10 , = 1 5 , and = 3 5 , assume + <1. Compute the unconditional variance E[h t].统计中等derivation未尝试面试订阅3093Steady Variance from Daily GARCH ParametersFor a GARCH(1,1) model h t=\omega+ r t-1 2+ h t-1 with \omega=1, = 1 10 , and = 4 5 , assume + <1. Compute the unconditional variance E[h t].统计中等derivation未尝试面试订阅3096Tomorrow Variance After a Large ShockIn a GARCH(1,1) model with \omega= 1 10 , = 1 5 , and = 7 10 , suppose the current squared return is r t 2=4 and the current conditional variance is h t=2. Compute h t+1 .统计简单derivation未尝试面试订阅3099Volatility Update from a Moderate ReturnIn a GARCH(1,1) model with \omega=1, = 3 20 , and = 3 5 , suppose the current squared return is r t 2=4 and the current conditional variance is h t=5. Compute h t+1 .统计简单derivation未尝试面试订阅3101Two-Step Forecast from Today’s VarianceFor a GARCH(1,1) process with \omega= 1 10 , = 1 5 , = 3 5 , suppose you already know the one-step-ahead conditional variance h t+1 =2. Compute E t[h t+2 ] and E t[h t+3 ].统计中等derivation未尝试面试订阅3103Two-Day Ahead Variance MeanFor a GARCH(1,1) process with \omega=1, = 1 10 , = 4 5 , suppose you already know the one-step-ahead conditional variance h t+1 =5. Compute E t[h t+2 ] and E t[h t+3 ].统计中等derivation未尝试面试订阅