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1796Signal Stationarity Classification 1A candidate signal is defined by X t = ε t + 0.3 ε t-1 . Is it weakly stationary?统计简单essay未尝试免费1797Signal Stationarity Classification 2A candidate signal is defined by X t = 0.2 t + ε t. Is it weakly stationary?统计中等derivation未尝试免费1798Signal Stationarity Classification 3A candidate signal is defined by X t = ε t + s t where s t is a fixed deterministic day-of-week pattern. Is it weakly stationary?统计简单derivation未尝试免费1799Signal Stationarity Classification 4A candidate signal is defined by X t = A cos(ω t) + B sin(ω t), where E[A]=E[B]=0, Var(A)=Var(B), Cov(A,B)=0. Is it weakly stationary?统计中等derivation未尝试免费1800Signal Stationarity Classification 5A candidate signal is defined by X t = t ε t. Is it weakly stationary?统计困难derivation未尝试面试订阅1801Measurement Noise Effect 1A latent stationary signal Y t has gamma(0) = 5 and gamma(1) = 2. You observe X t = Y t + eta t, where eta t is iid noise with variance 1.5 independent of Y t. What are gamma X(0) and gamma X(1)?统计简单essay未尝试免费1802Measurement Noise Effect 2A latent stationary signal Y t has gamma(0) = 8 and gamma(1) = 3. You observe X t = Y t + eta t, where eta t is iid noise with variance 2 independent of Y t. What are gamma X(0) and gamma X(1)?统计中等derivation未尝试免费1803Measurement Noise Effect 3A latent stationary signal Y t has gamma(0) = 6 and gamma(1) = -1. You observe X t = Y t + eta t, where eta t is iid noise with variance 4 independent of Y t. What are gamma X(0) and gamma X(1)?统计中等derivation未尝试免费1806Two-Point Sample Mean Variance 1A weakly stationary process has gamma(0) = 4 and gamma(1) = 1. What is Var((X 1 + X 2)/2)?统计简单essay未尝试免费1808Two-Point Sample Mean Variance 3A weakly stationary process has gamma(0) = 5 and gamma(1) = -1. What is Var((X 1 + X 2)/2)?统计中等数值题未尝试免费1811Validity or Stationarity Check 1Consider the proposal rho(h)=0.8 |h|. Is it valid from a stationarity / autocorrelation perspective?统计简单数值题未尝试免费1812Validity or Stationarity Check 2Consider the proposal rho(1)=1.2. Is it valid from a stationarity / autocorrelation perspective?统计中等derivation未尝试免费1813Validity or Stationarity Check 3Consider the proposal An AR(1) with phi = 1.03. Is it valid from a stationarity / autocorrelation perspective?统计中等数值题未尝试免费1814Validity or Stationarity Check 4Consider the proposal An AR(1) with phi = -0.6. Is it valid from a stationarity / autocorrelation perspective?统计困难derivation未尝试面试订阅1815Validity or Stationarity Check 5Consider the proposal An MA(1) claiming rho(1)=0.7. Is it valid from a stationarity / autocorrelation perspective?统计困难数值题未尝试面试订阅1816Why Differencing Helps a Trend but Not White NoiseA signal looks like deterministic trend plus short-memory noise. Why can first differencing help stationarity, while differencing plain white noise usually just injects a negative lag-1 correlation?统计简单essay未尝试免费1817Spurious Regression WarningWhy can regressing one drifting series on another produce a large R-squared and tiny p-values even when there is no economic relation?统计简单essay未尝试免费1818Why Ergodicity MattersWhy is ergodicity stronger than stationarity, and why do practitioners care about it when they average one long signal history?统计中等derivation未尝试免费1819Ljung-Box InterpretationWhat null hypothesis does the Ljung-Box test target in a return series, and what practical concern does rejection raise?统计中等derivation未尝试免费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