A Realtime Multivariate Statistical Analysis Method For Time Series

With the development of information society, time series is applied in manyindustries. So, the data mining is becoming the hot issue. How to analyze therealtime statistical measures and find the knowledge behind the data are worthy ofconcern. The statistical analysis of the time series can support the research ofmulti-variables time series. Before this, many researchers can propose manymethods which can only compute one statistical measures and are not suitable forothers. So, this research is very important for computing the realtime and accuratestatistical measures.We do some research about the base theory of the affine relationships. With thehelp of the matrix theory and the pseudo-inverse theory, we propose a newcomputing method of the affine relationships, which is suitable to compute thedynamical statistical measures of the realtime time series. The new computingmethod has these advantages:(1)it is suitable to compute the majority of dynamicalstatistical measures, such as mean, covariance, correlation coefficient, dot product,etc;(2)the relative error of the dynamical statistical measures which is computed byit is similar to the statical statistical measures;(3)in the face of the abnormal data, itcan perform well;(4) In the sliding window model, we build a multi-hierarchiesmethod, the summaries have such a good combined method that we can compute thedynamical statistical measures of a given time bucket.In this paper, the theoretical analysis of the affine relation is a theoreticalsupplement of the statical statistical measures. The experiments prove that the newcomputing method of the affine relationships can compute the dynamical statisticalmeasures. What’s more, consider the error level, temporal and spatial overhead, thispaper is no less than the foregoing methods which compute the statical statisticalmeasures. Besides, compared with the DFT technique which computes thedynamical correlation coefficient, the new computing method of the affinerelationship is suitable to compute the majory of the dynamic statistical measures.