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1820Measurement Noise Flattens ACFWhy can adding independent observation noise make an otherwise persistent signal look less autocorrelated?统计困难derivation未尝试面试订阅1823AR(1) Multi-Step Forecast 3A signal follows X t = -1 + 0.8 X (t-1) + e t with Var(e t) = 1 and current value X t = 3. What is the h = 4 step forecast E[X (t+4) | X t]?统计中等derivation未尝试免费1826MA(1) Lag-1 Correlation 1A microstructure noise model uses Y t = e t + 0.5 e (t-1). What is its lag-1 autocorrelation rho(1)?统计中等derivation未尝试面试订阅1829MA(1) Lag-1 Correlation 4A microstructure noise model uses Y t = e t + 1 e (t-1). What is its lag-1 autocorrelation rho(1)?统计中等derivation未尝试面试订阅1842ARMA Identification or Simplification 2You observe the diagnostic statement: ACF cuts after lag 1, PACF tails off. What is the correct modeling conclusion?统计中等derivation未尝试面试订阅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1861Long-Run Residual Variance 1A mean-reverting residual follows X (t+1) = 1/2 X t + epsilon (t+1) with Var(epsilon (t+1)) = 4. What is the stationary variance of X t?统计简单essay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