Plotly Stationarity
Recently we tested stationarity for a group of markets from US, Japan and UK. These are some visuals generated by the plotly for Stationarity data.
“In mathematics and statistics, a stationary process (or strict(ly) stationary process or strong(ly) stationary process) is a stochastic process whose joint probability distribution does not change when shifted in time. Consequently, parameters such as mean and variance, if they are present, also do not change over time.
Since Stationarity is an assumption underlying many statistical procedures used in time series analysis, non-stationary data is often transformed to become stationary. The most common cause of violation of Stationarity are trends in mean, which can be due either to the presence of a unit root or of a deterministic trend. In the latter case the process is called trend stationary process, stochastic shocks have only transitory effects, and the process is mean-reverting (on a mean which changes deterministically over time). On the contrary, in the first case stochastic shocks have permanent effects and the process is not mean-reverting. A trend stationary process is not strictly stationary, but can easily be made such by removing the underlying trend (function solely of time). Similarly, processes with one or more unit roots can be made stationary through differencing. An important type of non-stationary process that does not include a trend-like behavior is the cyclostationary process.
A “stationary process” is not the same thing as a “process with a stationary distribution”.[clarification needed] Indeed, there are further possibilities for confusion with the use of “stationary” in the context of stochastic processes; for example a “time-homogeneous” Markov chain is sometimes said to have “stationary transition probabilities”. Besides, all stationary Markov random processes are time-homogeneous.”
Source: Wikipedia