Zero mean transformation technique that is not effected by missing or removed data

Abstract

In the process of data transformation, if the mean of the transformed series is zero, such transformation techniques are known as zero mean transformation methods. Mean normalization and standardization are two most common methods that considered as zero mean transformation techniques. Those two methods consider only the dependent variable (y) for the transformation but not the independent variable (x). Therefore, this approach is suitable for time series that expected to follow y = c relation. Thus, usage of the said methods for time series with missing data that is expected to follow regression other than y = c (e.g.: y = mx + c), will destroys its original regression and lead to incorrect results. In this paper we represent a zero mean transformation method that transforms any time series into a series that considers both independent and dependent variables. Furthermore, the new technique is independent of the regression of the time series. Furthermore, the proposed technique is resilient to any time series with missing data or removed outliers (without replacement). The results shows that the proposed method is capable of transforming any time series into a series with zero mean despite of the influence of missing or removed outliers.