What Happens When We difference a trend stationary process?
In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root …
What is the difference between stationarity and differencing?
Stationarity and differencing. Statistical stationarity: A stationary time series is one whose statistical properties such as mean, variance, autocorrelation, etc. are all constant over time. Most statistical forecasting methods are based on the assumption that the time series can be rendered approximately stationary (i.e.,…
Which is the best description of a stationary process?
In mathematics and statistics, a stationary process ( a.k.a. 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. Consequently, parameters such as mean and variance also do not change over time.
When do time series become stationary by differencing?
Time series that can be made stationary by differencing are called integrated processes. Specifically, when D differences are required to make a series stationary, that series is said to be integrated of order D, denoted I(D). Processes with D ≥ 1 are often said to have a unit root.
What causes non stationary data to become stationary?
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 is a trend in the mean, which can be due either to the presence of a unit root or of a deterministic trend.