Question

Please explain details that what is the difference between “difference stationary” and “trend stationary”

Answer 1

Trend stationary : Once the trend is estimated and removed from the data, the residual series is a stationary stochastic process.

​​​​​​​difference stationary: The mean trend is stochastic. Differencing the series D times yields a stationary stochastic process.

The distinction between a deterministic and stochastic trend has important implications for the long-term behavior of a process:Ts

Timeeries with a deterministic trend always revert to the trend in the long run (the effects of shocks are eventually eliminated). Forecast intervals have constant width.T

Timeseries with a stochastic trend never recover from shocks to the system (the effects of shocks are permanent). Forecast intervals grow over time.

Model of trend stationary is given as

and diffence stationary model is given as

Take a time series, regress it on time taken as a trend variable. Then if the resulting error becomes stationary after the process, the time series is a trend stationay time series. Otherwise, if after taking differences of the time series it becomes stationary, then it is said to be a differenced stationary time series. However, differencing may be done once, twice etc sometimes to make it stationary depending on the order of integration of the time series.