3 added 13 characters in body edited Aug 18 '15 at 22:26 ekvall 3,65911 gold badge1010 silver badges3333 bronze badges Neither is true. Consider the two following examples: (1) Let $$\xi \sim N(0,1)$$ and define the stochastic process $$X_i=\xi, i=1,2,\dots$$. it's easy to check that this process is (strongly) stationary, while at the same time $$\mathrm{Cov}(X_i, X_j)=1, \forall i,j$$. (2) Consider a stochastic process consisting of independent Gaussian variables $$X_i \sim N(0, i), i=1,2,\dots$$. This process is clearly not stationary, but there is nothe autocorrelation is zero for all lags since the variables are independent. Neither is true. Consider the two following examples: (1) Let $$\xi \sim N(0,1)$$ and define the stochastic process $$X_i=\xi, i=1,2,\dots$$. it's easy to check that this process is (strongly) stationary, while at the same time $$\mathrm{Cov}(X_i, X_j)=1, \forall i,j$$. (2) Consider a stochastic process consisting of independent Gaussian variables $$X_i \sim N(0, i), i=1,2,\dots$$. This process is clearly not stationary, but there is no autocorrelation since the variables are independent. Neither is true. Consider the two following examples: (1) Let $$\xi \sim N(0,1)$$ and define the stochastic process $$X_i=\xi, i=1,2,\dots$$. it's easy to check that this process is (strongly) stationary, while at the same time $$\mathrm{Cov}(X_i, X_j)=1, \forall i,j$$. (2) Consider a stochastic process consisting of independent Gaussian variables $$X_i \sim N(0, i), i=1,2,\dots$$. This process is clearly not stationary, but the autocorrelation is zero for all lags since the variables are independent. 2 deleted 4 characters in body edited Aug 18 '15 at 19:18 ekvall 3,65911 gold badge1010 silver badges3333 bronze badges Neither is true. Consider the two following examples: (1) Let $$\xi \sim N(0,1)$$ and define the stochastic process $$X_i=\xi, i=1,2,\dots$$. it's easy to check that this process is (strongly) stationary, while at the same time $$\mathrm{Cov}(X_i, X_j)=1, \forall i,j$$. (2) Consider a stochastic process consisting of independent Gaussian variables $$X_i \sim N(0, i), i=1,2,\dots$$. This process is clearly not stationary, but there is no autocorrelation since the variables are independent. (1) Let $$\xi \sim N(0,1)$$ and define the stochastic process $$X_i=\xi, i=1,2,\dots$$. it's easy to check that this process is (strongly) stationary, while at the same time $$\mathrm{Cov}(X_i, X_j)=1, \forall i,j$$. (2) Consider a stochastic process consisting of independent Gaussian variables $$X_i \sim N(0, i), i=1,2,\dots$$. This process is clearly not stationary, but there is no autocorrelation since the variables are independent. Neither is true. Consider the two following examples: (1) Let $$\xi \sim N(0,1)$$ and define the stochastic process $$X_i=\xi, i=1,2,\dots$$. it's easy to check that this process is (strongly) stationary, while at the same time $$\mathrm{Cov}(X_i, X_j)=1, \forall i,j$$. (2) Consider a stochastic process consisting of independent Gaussian variables $$X_i \sim N(0, i), i=1,2,\dots$$. This process is clearly not stationary, but there is no autocorrelation since the variables are independent. Neither is true. Consider the two following examples: (1) Let $$\xi \sim N(0,1)$$ and define the stochastic process $$X_i=\xi, i=1,2,\dots$$. it's easy to check that this process is (strongly) stationary, while at the same time $$\mathrm{Cov}(X_i, X_j)=1, \forall i,j$$. (2) Consider a stochastic process consisting of independent Gaussian variables $$X_i \sim N(0, i), i=1,2,\dots$$. This process is clearly not stationary, but there is no autocorrelation since the variables are independent. 1 answered Aug 18 '15 at 18:45 ekvall 3,65911 gold badge1010 silver badges3333 bronze badges Neither is true. Consider the two following examples: (1) Let $$\xi \sim N(0,1)$$ and define the stochastic process $$X_i=\xi, i=1,2,\dots$$. it's easy to check that this process is (strongly) stationary, while at the same time $$\mathrm{Cov}(X_i, X_j)=1, \forall i,j$$. (2) Consider a stochastic process consisting of independent Gaussian variables $$X_i \sim N(0, i), i=1,2,\dots$$. This process is clearly not stationary, but there is no autocorrelation since the variables are independent.