Proving that this process is weakly-stationary [duplicate]

1. How can you prove that a time series is weakly stationary?
2. What is a weakly stationary process?
3. What is the difference between strict stationarity and weak stationarity?

How can you prove that a time series is weakly stationary?

A time series is considered as weakly stationary if the associated mean and covariance function do not vary with respect to time. That is to say, the original time series has statistical properties similar to those of the 'time-shifted' series.

What is a weakly stationary process?

Weak-Sense Stationary Processes: Here, we define one of the most common forms of stationarity that is widely used in practice. A random process is called weak-sense stationary or wide-sense stationary (WSS) if its mean function and its correlation function do not change by shifts in time.

What is the difference between strict stationarity and weak stationarity?

A time series model which is both mean stationary and covariance stationary is called weakly stationary. A time series model for which all joint distributions are invariant to shifts in time is called strictly stationary.