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1821AR(1) Multi-Step Forecast 1A signal follows X t = 0 + 0.6 X (t-1) + e t with Var(e t) = 2 and current value X t = 10. What is the h = 3 step forecast E[X (t+3) | X t]?统计简单数值题未尝试免费1822AR(1) Multi-Step Forecast 2A signal follows X t = 4 + 0.7 X (t-1) + e t with Var(e t) = 1.5 and current value X t = 8. What is the h = 2 step forecast E[X (t+2) | X t]?统计简单derivation未尝试免费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