An early attempt to produce a spectral estimator with better variance properties than the periodogram was to truncate the summation in at m   The idea is to discard estimates of the ACVS for which...

An early attempt to produce a spectral estimator with better variance properties than the periodogram was to truncate the summation in at m <>

The idea is to discard estimates of the ACVS for which there are relatively little data. This estimator is known as the truncated periodogram. Show that Sˆ (TP)(·) can be regarded as a special case of a lag window spectral estimator, and determine its lag window and its smoothing window. Argue that the truncated periodogram need not be nonnegative at all frequencies.