- Stationarity Time Series is a Series whose properties do not depend on the time at which the series is observed
- We can also say that the Stationarity Properties of Data Generating Process of a certain time-series do not change over time
- As a result we can say that the stationarity time series do not use to have Trend or Seasonality patterns as their existence violates the stationarity assumptions
- White Noise process is always a stationarity time series as it is always look pretty much the same at any point of time
- So we can also add that the Time-Series without the Trend and Seasonality but with cyclic behaviour can still be stationarity because the cycles are not of fixed length. So unless we explicitly look for Time-Series, we can not be sure where the peaks and troughs of the cycles are location
For a Time-Series to be classified as covariance Stationarity (weak stationarity), it must satisfy following 3 conditions
- The Mean of the Series must be contant
- The Variance of the Series must be finite and constant
- The Covariance between the periods of identical distance must be constant
It will not be surprising to say that Stationarity is a desired characteristic of time-series as it makes modeling and extrapolating (forcasting) into the future more feasible. It is because the stationarity is easier to predict than the non-stationarity as its statistical properties will be the same in the future as they has been in the past
The drawbacks of non-stationarity data are:
- Variance can be misspecified by the model
- Worse model fit, resulting in worse forecasting
- The can not leverage valuable time-dependent patterns in the data
Thought Stationarity is a desired characteristic, but it can not be used everywhere, or we can say it is not applicable to all statistical models
We would like data to be stationairy when we are working with models which are auto-regressive like (AR, ARMA,ARIMA)
But then there are models who are not dependent on stationarity time-series like those depends on time-series decomposition (like exponential smoothing methods, Facebook’s Prophet)
Below are the methods used to check the stationarity of time-series data:
- The Augmented Dickey-Fuller (ADF) test
- The Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test
- Plots of the (partial) autocorrelation function (PACF/ACF)
