HEAVY-TAILED DISTRIBUTION AND LOCAL LONG MEMORY IN TIME SERIES OF MOLECULAR MOTION ON THE CELL MEMBRANE

摘要

The joint presence of heavy-tailed distribution and long memory in time series alwaysnleads to certain trouble in correctly obtaining the statistical characteristics for timenseries modeling. These two properties i.e., heavy-tailed distribution and long memory,ncannot be neglected in time series analysis, because the tail thickness of the distributionnand long memory property of the time series are critical in characterizing the essencenof the resulting natural or man-made phenomenon of the time series. Meanwhile, thenfluctuation of the varying local long memory parameter may be used to capture theninternal changes which underlie the externally observed phenomenon. Therefore, in thisnpaper, we proposed to use the variance trend, heavy-tailed distribution, long memory,nand local long memory characteristics to analyze a time series recorded as in [1] fromntracking the jumps of individual molecules on cell membranes. The tracked moleculesnare Class I major histocompatibility complex (MHCI) expressed on rat hepatoma cells.nThe analysis results show that the jump time series of molecular motion on the cellnmembrane obviously has both heavy-tailed distribution and local long memory characteristics.nThe tail heaviness parameters, long memory parameters, and the local longnmemory parameters of ten MHCI molecular jump time series are all summarized withntables and figures in the paper. These reported tables and figures are not only interestingnbut also important in terms of additional novel insights and characterization of the timenseries under investigation