In Time Series, the Bartlett window is a weighted moving average transformation used to smooth the periodogram values. In the Bartlett window (Bartlett, 1950) the weights are computed as:

wj = 1-(j/p) (for j=0 to p)

w-j = wj (for j¹0)

where p = (m-1)/2 and m is the width of the moving average window (which must be an odd number).

This weight function will assign the greatest weight to the observation being smoothed in the center of the window, and increasingly smaller weights to values that are further away from the center. Note also that the Time Series module will standardize the weights so that they sum to 1.

See also, Basic Notations and Principles and Data Windows and Spectral Density Estimates.