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The SPECTRA Procedure |
Kernels |
Kernels are used to smooth the periodogram by using a weighted moving average of nearby points. A smoothed periodogram is defined by the following equation.
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where is the kernel or weight function. At the endpoints, the moving average is computed cyclically; that is,
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The SPECTRA procedure supports the following kernels. They are listed with their default bandwidth functions.
Bartlett: KERNEL BART
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Parzen: KERNEL PARZEN
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Quadratic spectral: KERNEL QS
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Tukey-Hanning: KERNEL TUKEY
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Truncated: KERNEL TRUNCAT
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A summary of the default values of the bandwidth parameters, c and e, associated with the kernel smoothers in PROC SPECTRA are listed below in Table 25.2:
Kernel |
c |
e |
Bartlett |
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Parzen |
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quadratic |
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Tukey-Hanning |
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truncated |
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See Andrews (1991) for details about the properties of these kernels.
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