Question

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 remains unchanged. b. there is serial correlation between the error terms of successive time periods and the explanatory variables and the error terms have positive covariance. c. there is no serial correlation between the error terms of successive time periods and the explanatory variables and the error terms have positive covariance. d. any collection of random variables in a sequence is taken and shifted ahead by h time periods; the joint probability distribution changes.

Answer 1

B.any collection of random variables in a sequence is taken and shifted ahead by htime periods, the joint probability distribution remains unchanged

Explanation:

In most of the time series techniques , there is usually a common assumption that data are stationary. A stationary process can be regarded as one that has properties such as variance mean, variance as well as autocorrelation structure not changed over time. The properties is independent as regards the time the series is observed.

✓ Time series that has trends or seasonality cannot be regarded as stationary, because the value of the time series which exist in different times will be affected by the trend and seasonality.

✓A white noise series can be regarded as stationary because the time you observe it does not matter, it will always look much the same at all point in time.

✓ It should be noted that process is stationary if any collection of random variables in a sequence is taken and shifted ahead by htime periods, the joint probability distribution remains unchanged