Het gebruik van bewegende gemiddelden voor de analyse van een economische grafiek

Part A of this paper is devoted to U discussion of the properties of linear operators, briefly called ‘linors’. To the well known series of operators Δ= (1,‐2,1), Δ4= (1,‐4,6‐4,1) etc, a series S2= (1,2,1), S4= (1,4,6,4,1) etc. is made to correspond. The series Δ2k is shown to have a detrimental influence on the trend in a time series, whereas the series S2k will retain the trend but remove random errors and cyclical variations. By combination of Δ‐ and S‐linors a linor is derived which may reasonably be assumed to retain the trend and the cyclical variations but to remove the random errors. Next a simple type of moving average operator is deduced which is adopted as giving the trend alone. By a systematic application of these linors a time series can be split up into a trend, a cyclical vuriation, and a random rest. In part B this analysis is performed with two different economic time‐series, while in part C some general considerutions concerning the degree of regression, the reduction of errors, and the smoothness and fitting of linear operators are developed.