A process is stationary if:
A)any collection of random variables in a sequence is taken and shifted ahead by h time periods; the joint probability distribution changes.
B)any collection of random variables in a sequence is taken and shifted ahead by h time periods, the joint probability distribution remains unchanged.
C)there is serial correlation between the error terms of successive time periods and the explanatory variables and the error terms have positive covariance.
D)there is no serial correlation between the error terms of successive time periods and the explanatory variables and the error terms have positive covariance.

Question

Quizplus · Accepted Answer

A stationary process is one whose statistical properties, such as mean and variance, remain constant over time. When any collection of random variables in a sequence is taken and shifted ahead by h time periods, the joint probability distribution remains unchanged, indicating that the process is stationary. Option B correctly captures this property. Option A is incorrect since a stationary process should not exhibit any change in statistical properties upon shifting. Option C is incorrect since a stationary process is not expected to have serial correlation between error terms or explanatory variables, and positive covariance is not a defining property of stationarity. Option D is also incorrect since a stationary process should not exhibit serial correlation between error terms or explanatory variables, and positive covariance is not a defining property of stationarity.

A Process Is Stationary If