In Time Series, the Parzen window is a weighted moving average transformation used to smooth the periodogram values. In the Parzen window (Parzen, 1961), for each frequency, the weights for the weighted moving average of the periodogram values are computed as:

wj = 1-6*(j/p)2 + 6*(j/p)3 |
for j = 0 to p/2 |

wj = 2*(1-j/p)3 |
for j = p/2 + 1 to p |

w-j = wj |
for j¹0 |

where p = (m-1)/2

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.