Strictly stationary and weakly stationary

1. What is the difference between strict stationarity and weak stationarity?
2. What is strictly stationary?
3. What does weakly stationary mean?
4. Does strict stationarity imply weak stationarity?

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.

What is strictly stationary?

In mathematics and statistics, a stationary process (or a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose unconditional joint probability distribution does not change when shifted in time.

What does weakly stationary mean?

Weak form of stationarity is when the time-series has constant mean and variance throughout the time. Let's put it simple, practitioners say that the stationary time-series is the one with no trend - fluctuates around the constant mean and has constant variance.

Does strict stationarity imply weak stationarity?

Definition 3.2.6 (Weak Stationarity)

Given the assumption that all first and second order moments exist and are finite, strict stationarity clearly implies weak stationarity.