A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²)

Question

A stochastic process {x_t: t = 1,2,….} with a finite second moment [E(x_t²)< ∞] is covariance stationary if: A)E(x_t)is variable,Var(x_t)is variable,and for any t,h ≥ 1,Cov(x_t,x_t+h)depends only on 'h' and not on 't'. B)E(x_t)is variable,Var(x_t)is variable,and for any t,h ≥ 1,Cov(x_t,x_t+h)depends only on 't' and not on h. C)E(x_t)is constant,Var(x_t)is constant,and for any t,h ≥ 1,Cov(x_t,x_t+h)depends only on 'h' and not on 't'. D)E(x_t)is constant,Var(x_t)is constant,and for any t,h ≥ 1,Cov(x_t,x_t+h)depends only on 't' and not on 'h'.

Quizplus · Accepted Answer

A stochastic process is said to be covariance stationary if its mean and variance are constant over time, and the covariance between any two time points only depends on the time lag between them and not on the actual time points. Therefore, option C is the correct option as it satisfies all the conditions for a covariance stationary process. Options A and B have a variable mean and variance, making them non-stationary, and option D has a covariance that depends only on time and not on the lag, which is also not stationary.

A Stochastic Process {Xt: T = 1,2,…

A Stochastic Process {X_t: T = 1,2,…