## 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 R_{max} of a_{m}ax - a_{min} and S_{n} - a_{min}^{∗}n and that of R_{min} of a_{max} - a_{min} and a_{max}^{∗}n - S_{n} are always equal to 2/n, where a_{max} is the maximum element, a_{min} is the minimum element and S_{n} 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, R_{max} > 2/n and R_{min} > 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 +k_{1}) and 2/n^{∗} (1 + k2), respectively, where k_{1} > k_{2} and 0 <k_{1} <n/2-1. Given this relation and transformation technique, which transforms data into the form y = c, we show that removing all data that do not agree with linear fit is possible. Furthermore, the method is independent of the number of data points, missing data, removed data points and nature of distribution (Gaussian or non-Gaussian) of outliers, noise and clean data. These are major advantages over the existing linear fit methods. Since having a perfect linear relation between two variables in the real world is impossible, we used artificial data sets with extreme conditions to verify the method. The method detects the correct linear fit when the percentage of data agreeing with linear fit is less than 50%, and the deviation of data that do not agree with linear fit is very small, of the order of ±10∼^{4}%. The method results in incorrect detections only when numerical accuracy is insufficient in the calculation process.

Original language | English |
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Article number | e0141486 |

Journal | PLoS ONE |

Volume | 10 |

Issue number | 11 |

DOIs | |

State | Published - 1 Nov 2015 |