Before fitting any existing model to time-series data we check for different things
- Stationarity of time series: Stationarity of time series is ensured by three properties . A pictorial depiction of these properties is shown at link
- The mean of time-series (xt) is the same for all xt .
- The variance of time-series (xt) is the same for all xt .
- The covariance (and also correlation) between xt and xt-h is the same for all t.
We care about stationarity because most time-series models assume stationarity. Also, a time-series can be stationarized by detrending and differencing.