Howtosignalprocessing
- What is the difference between weak and strict stationarity?
- What is strict stationarity?
- Does strict stationarity imply weak stationarity?
- What is meant by weak stationarity?
What is the difference between weak and strict 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 strict stationarity?
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.
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.
What is meant by weak stationarity?
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.
