Time Series Analysis - Specify the Smoothing Weights

Select the User-defined option button in the Smoothing window group box on the Transformations of Variables dialog box - Fourier tab and click the adjacent    button to display the Specify the smoothing weights dialog.

Weight 1, 2, 3... Enter values in the Weights boxes to specify the weights to be used for the smoothing of the periodogram values. Note that the weights are always be standardized so that they sum to 1. For example, if you entered 1 2 3 2 1 in the Weights boxes, they will be converted to: 1/9 2/9 3/9 2/9 1/9 (so that they add up to 1).

As described in greater detail in Spectrum (Fourier) Analysis, the periodogram values themselves are subject to substantial random fluctuation. A clearer picture of underlying periodicities often only emerges when examining the spectral densities, that is, the frequency regions, consisting of many adjacent frequencies, that contribute most to the overall periodic behavior of the series. The spectral density estimates are computed by smoothing the periodogram values with a weighted moving average. The standard weight functions assign the greatest weight to the observation in the center of the window, and (symmetrically) decreasing weights to the observation further away from the center (this also often helps to alleviate the problem of leakage; refer to Spectrum Analysis Basic Notation and Principles - The Problem of Leakage for details).