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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1828MA(1) Lag-1 Correlation 3A microstructure noise model uses Y t = e t + -0.4 e (t-1). What is its lag-1 autocorrelation rho(1)?统计简单数值题未尝试免费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1831MA(1) Invertibility Check 1An MA(1) execution-noise model uses theta = 0.4. Is the model invertible?统计简单数值题未尝试免费1833MA(1) Invertibility Check 3An MA(1) execution-noise model uses theta = -0.7. Is the model invertible?统计中等数值题未尝试面试订阅1836AR(1) Forecast Error Variance 1For the AR(1) model X t = phi X (t-1) + e t with phi = 0.6 and Var(e t) = 1, what is the h = 3 step forecast error variance?统计简单derivation未尝试免费1838AR(1) Forecast Error Variance 3For the AR(1) model X t = phi X (t-1) + e t with phi = 0.5 and Var(e t) = 2.25, what is the h = 4 step forecast error variance?统计中等essay未尝试面试订阅1841ARMA Identification or Simplification 1You observe the diagnostic statement: ACF tails off geometrically, PACF cuts after lag 1. What is the correct modeling conclusion?统计简单数值题未尝试免费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1843ARMA Identification or Simplification 3You observe the diagnostic statement: Both ACF and PACF tail off. What is the correct modeling conclusion?统计中等derivation未尝试面试订阅1844ARMA Identification or Simplification 4You observe the diagnostic statement: AIC prefers ARMA(2,1) but BIC prefers ARMA(1,1). What is the correct modeling conclusion?统计简单derivation未尝试免费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