The Autocorrelation Function (ACF) Questions with complete solution 2023/2024

The Autocorrelation Function (ACF) Questions with complete solution 2023/2024The j-th order autocorrelation function is defined as - correct answer rho(j) = gamma(j)/gamma(0) = ([E(X(t)-mew)*E(X(t-j)-mew)])/(E[(X(t) - mew)^2]) = (Cov(X(t),X(t-j))/Var(X(t) for j = 0,1,2,... with -1 <= rho(j) <= 1 The plot of rho(j) against j = 0,1,2,... is called - correct answer the correlogram For a stationary ergodic process, the ACF can be estimated by the sample moments as follows - correct answer y bar = (1/T) * Summation from t=1 to T of y(t) sigma hat^2 = (1/T) * Summation from t=1 to T of (y(t) - y bar)^2 for each j: r(j) = (Summation from t=j+1 to T of (y(t)-y bar)*(y(t-j)-y bar))/(Summation from t=1 to T of (y(t)-y bar)^2) Sample variance of r(j): Var(r(j