A window is a fixed-length subset of consecutive observations of a time series. The window is moved along the time series at a constant rate. AKA "rolling window".

A window is a fixed-length subset of consecutive observations of a time series. The window is moved along the time series at a constant rate. Also known as a "rolling window".

A basic use of a moving window is to inspect stationarity of a time series. Descriptive statistics of a stationary series would change little from one window to another, while those of a nonstationary series may change a lot.

More popular uses of a moving window are to evaluate predictive accuracy, stability and other properties of a model, as well as to select a model from several candidates. A model is reestimated and a forecast is made in each window, for a number of windows. The forecasts are compared to the realizations to asses their accuracy. Unlike in-sample forecast evaluation, a moving window offers a fair evaluation of forecast accuracy because future data are not used in estimation of the model parameters.

A moving window offers a form of cross validation for time series models when model errors cannot be assumed to be i.i.d. over time.