A Simple Method of Trend Construction
Conrad E. V. Leser · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1961
SUMMARY The principle adopted here in the construction of a trend for a time series consists in minimizing a linear combination of two sums of squares, of which one refers to the second differences of the trend values, the other to the deviations of the observations from the trend values. Properties of the general solution are deduced, and the solution is explicitly obtained for up to 7 observations. In the special case in which the sum of the two sums of squares is minimized, the exact solution is derived for up to 15 observations. An approximation formula, suitable for practical use when there are 8 or more observations, is also given. The method is illustrated by examples, in which it is applied to an artificially constructed and to an actual time series.