Moving-weighted-average smoothing extended to the extremities of the data. I. Theory
- 1 January 1981
- journal article
- research article
- Published by Taylor & Francis in Scandinavian Actuarial Journal
- Vol. 1981 (1) , 39-55
- https://doi.org/10.1080/03461238.1981.10413730
Abstract
The use of a symmetrical moving weighted average of 2m + 1 terms to smooth equally spaced observations of a function of one variable does not yield smoothed values of the first m and the last m observations, unless additional data beyond the range of the original observations are available. By means of analogies to the Whittaker smoothing process and some related mathematical concepts, a natural method is developed for extending the smoothing to the extremities of the data as a single overall matrix-vector operation having a well defined structure, rather than as something extra grafted on at the ends. The matrix approach is shown to be equivalent to an extrapolation algorithm.Keywords
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