Universal linear fit identification: A method independent of data, outliers and noise distribution model and free of missing or removed data imputation

Abstract

Dataprocessing requires a robust linear fit identification method. In this paper, we introduce a non-parametric robust linear fit identification method for time series. The method uses an indicator 2/n to identify linear fit, where n is number of terms in a series. The ratio Rmax of amax - amin and Sn - amin∗n and that of Rmin of amax - amin and amax∗n - Sn are always equal to 2/n, where amax is the maximum element, amin is the minimum element and Sn is the sum of all elements. If any series expected to follow y = c consists of data that do not agree with y = c form, Rmax > 2/n and Rmin > 2/n imply that the maximum and minimum elements, respectively, do not agree with linear fit. We define threshold values for outliers and noise detection as 2/n∗ (1 +k1) and 2/n∗ (1 + k2), respectively, where k1 > k2 and 0