A simple example of a smoother is the moving average procedure. It is based on averaging elements closest in time to the current time. Mathematically this can be expressed by the following simple formula:
where
- is the input of the smoother, the original time series;
- is the output of the smoother, the smoothed time series;
- is the size of the smoothing window.
The parameter ( or the size of the window) determines the degree of smoothing: the greater , the smoother the output time series .
The ability of this simple smoother to reduce higher frequencies is quite poor. Therefore in time series analysis and other applications other classes of smoothers are normally used.