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1845ARMA Identification or Simplification 5You observe the diagnostic statement: (1-0.5L) X t = (1-0.5L) e t. What is the correct modeling conclusion?统计困难essay未尝试面试订阅1846Residual After 2 Rebalances 1A residual spread follows X (t+1) = 2/3 X t + epsilon (t+1) with E[epsilon (t+1)] = 0. If today's residual is 9 bp, what is E[X 2 | X 0 = 9 bp]?统计简单derivation未尝试免费1851Cumulative Mean-Reversion Carry 1A desk is short a positive residual and books one unit of carry each day equal to that day's expected residual. If X (t+1) = 3/4 X t + epsilon (t+1) with zero-mean shocks and X 0 = 12 bp, what is the total expected carry over the next 3 days?统计简单essay未尝试免费1856Horizon Risk Budget Ratio 1A stationary mean-reverting spread obeys X (t+1) = 1/2 X t + epsilon (t+1), where Var(epsilon (t+1)) = 4. Starting from the current level, what fraction of the same-horizon random-walk forecast-error variance does the 4-step mean-reverting forecast-error variance represent?统计简单derivation未尝试免费1866RW Versus MR Diagnosis 1A residual's variance keeps growing roughly linearly with horizon and never appears to plateau. Which description fits better: random walk or mean reversion?统计简单essay未尝试免费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1871Hidden Launch Mix from Survivor Panel 1A fund database currently shows 54 live statistical-arbitrage funds and 18 live macro funds. Historical one-year survival rates for these styles were 90% for statistical-arbitrage and 60% for macro. Assuming the current live panel comes from one launch cohort, what fraction of the original launches were macro funds?统计简单essay未尝试免费1872Hidden Launch Mix from Survivor Panel 2A live manager database now contains 32 market-neutral funds and 24 credit relative-value funds. Historical survival rates for those styles were 80% and 50%, respectively. What fraction of the original launches were credit relative-value funds?统计简单essay未尝试面试订阅1873Displayed High-Turnover Share BiasA live fund panel shows 45 low-turnover funds and 15 high-turnover funds. Historical survival rates were 90% for low-turnover funds and 30% for high-turnover funds. By how many percentage points does the displayed live panel understate the original share of high-turnover launches?统计简单essay未尝试免费1874Original Launch Ratio from Differential SurvivalToday’s database contains 28 live discretionary funds and 42 live systematic funds. Historical survival rates were 40% for discretionary funds and 70% for systematic funds. What was the original launch ratio of discretionary funds to systematic funds?统计简单essay未尝试面试订阅1875Regional Launch Share ReconstructionA current hedge-fund database shows 36 live Asia funds and 24 live Europe funds. Historical survival rates were 60% for Asia funds and 80% for Europe funds. What fraction of the original launches were Asia funds?统计简单essay未尝试面试订阅1876Track-Record Age Bias 1As of end-2026, a database contains 45 surviving funds launched in 2024, 20 surviving funds launched in 2022, and 9 surviving funds launched in 2020. The corresponding survival rates were 90%, 50%, and 30%. By how many years does the average age in the live panel understate the average age across all original launches?统计中等essay未尝试面试订阅1877Track-Record Age Bias 2At end-2027, a manager database contains 54 surviving funds launched in 2026, 24 surviving funds launched in 2024, and 10 surviving funds launched in 2022. The survival rates for those vintages were 90%, 60%, and 40%. How many years does the live-panel average age understate the average age across all original launches?统计中等essay未尝试免费1878Track-Record Age Bias 3As of end-2028, a database shows 24 live funds launched in 2020 and 28 live funds launched in 2026. The survival rates for those two vintages were 40% and 80%, respectively. By how many years does the live-panel average age understate the true launch-universe average age?统计中等essay未尝试免费1879Full-Universe Average Launch YearAt end-2026, a live panel contains 18 funds launched in 2017 and 24 funds launched in 2021. The survival rates for those vintages were 30% and 80%, respectively. What was the average launch year across all original launches?统计中等essay未尝试面试订阅1880Pre-2020 Share Hidden by AttritionA database of currently live funds contains 12 funds launched before 2020 and 36 funds launched in or after 2020. The survival rates for those two groups were 25% and 75%, respectively. What share of the original launches occurred before 2020?统计简单essay未尝试面试订阅1881True Turnover of the Launch UniverseAmong currently live funds, 40 are low-turnover and 20 are high-turnover. Historical survival rates were 80% for low-turnover funds and 40% for high-turnover funds. Suppose low-turnover funds average 60% annual turnover and high-turnover funds average 180% annual turnover. What was the average turnover across the original launch universe?统计简单essay未尝试免费1882Momentum Loading Hidden by Differential SurvivalA live panel contains 30 value-oriented funds and 10 momentum-oriented funds. The historical survival rates of those styles were 75% and 25%, respectively. Suppose the average momentum loading is -0.1 for value-oriented funds and 0.7 for momentum-oriented funds. What was the average momentum loading across the original launches?统计简单essay未尝试免费1883Average Gross Leverage at LaunchA 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 leverage across the original launches?统计简单essay未尝试面试订阅