Criteria for Weighted Moving-Mean Method

摘要

The moving-mean method is one of the conventional approaches for trend-extraction from a data set. It is usually applied in an empirical way. The smoothing degree of the trend depends on the selections of window length and weighted coefficients, which are associated with the change pattern of the data. Are there any uniform criteria for determining them? The present article is a reaction to this fundamental problem. By investigating many kinds of data, the results show that: 1) Within a certain range, the more points which participate in moving-mean, the better the trend function. However, in case the window length is too long, the trend function may tend to the ordinary global mean. 2) For a given window length, what matters is the choice of weighted coefficients. As the five-point case concerned, the local-midpoint, local-mean and global-mean criteria hold. Among these three criteria, the local-mean one has the strongest adaptability, which is suggested for your usage.