A TEST TO INVESTIGATE VARIOUS FACTORS OF SIGHTING ERROR
Abstract
Applied Mathematics and S atistics Lab., Stanford U., Calif. TREND ELIMINATION BY MOVING-AVERAGE AND VARIATEDIFFERENCE FILTERS, by J. Durbin. 24 Aug 61, 20p. 7 refs. (Technical rept. no. 9) (Grant DA-ORD-43) (AROD rept. no. 2025:8) Uncla sifie report No automatic release to Foreign Nationals. D SCRIPTORS: ( tatistical analysis, *Statis tical processes, *Lea t squares method Polynomials, Operator (Mathematics), Topology, Fourier analysis, Series.) Identifiers: Filters (Mathematics). The use of a variat -differ nce or movingaverage filter is s own to be equivalen to t subtraction of a low-order polynomial. Since the main reason for using such a filter is usually a disbelief in the adequacy of a loworder polynomial to represent trend satisfactorily, this seems a rather discouraging conclusion. However, when examined further it is found that the nature of the fitting of t e polynomial achieved by the u e of one of these filters i such that a r pidly converging Fourier expansion is obtained of any residu l trend left in the series. The effect is that the concentration of residual trend in the low frequ ncies of the spectrum is likely to be much greater than is achi ved by o her methods of fitting polynomial such as le st squares. Consequently, the distortion of estimates of the spectrum due to the presence of residual trend is likely to be small except in the imm diate neighborhood of the origin. This is a v ry desirable property. T O SIMPLIFY THE EXPOSITION, IT IS ASSUMED THROUGHOUT THAT THE PERIODIC TERM ST IS ZERO. However, it can be shown that results similar to t o e obtai d for p rio ogra or i es apply to the estimation of season l co t nts d other periodic component.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1961
- Accession Number
- AD0268891
Entities
People
- L. F. Moore