1. Stationarity
- Data are stationary when the parameters of the data generating process do not change over time.
- if you naively use certain statistics on a non-stationary data set, you will get garbage results.
Testing for Stationarity
adfuller: The Augmented Dickey-Fuller test can be used to test for a unit root in a univariate process in the presence of serial correlation.
- In each individual case the test may or may not pick up subtle effects like this.
2. Integration
The reason returns are usually used for modeling in quantitive finance is that they are far more stationary than prices. This makes them easier to model and returns forecasting more feasible. Forecasting prices is more difficult, as there are many trends induced by their I(1) integration. Even using a returns forecasting model to forecast price can be tricky, as any error in the returns forecast will be magnified over time.