Case study on measuring central tendancy of a set of time series based on discrete Haar wavelet

Abstract

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Knowledge discovery in data has been emerged in a rapid phase with the necessity of effective and efficient methods to extract beneficial information from data and simulated results. With this background, this study focuses on investigating two methods used as measures of central tendency for set of time series or mean series and tamed series. Average series, the most commonly using method of summarizing set of time series may limit the interpretations on variability as some patterns may be vanished because of its solid nature. In this concern, tamed series can be used as an alternative to the average series, a measure of central tendency with a stochastic description. The proposed method of taming is based on Haar wavelet generated by taking the deviation of two time series as a spectrum called decomposed error spectrum (DES-W) and further manipulations to obtain a measure of central tendency. The functionality of decomposing used in DES-W evades the link between consecutive data points lying in different couples, leading to different spectrums, hence different tame series, for the same set of input time series. The order of concern of time series in the taming process is another fact courses to varied outcomes, which notifies the sensitivity to the case specification, intimating the applicability to stochastic models.