Discrete-time scale invariant systems: Relation to long-range dependence and farima models

A discrete-time version of linear scale-invariant systems was provided by Zhao and Rao. This formulation, called a DLSI system, was derived using a continuous dilation operator in discrete-time as a direct analog of the continuous-time linear scale-invariant system formulation of Wornell. While simulations had shown that DLSI systems were capable of generating self-similar data such as those found in network traffic, answers to questions regarding their relationship to other models had not been found. This paper investigates such relationships. It derives results establishing parameter ranges for DLSI systems that give rise to long-range dependent outputs for white noise inputs. Furthermore, it shows that the basic DLSI system is expressible as a special fractional ARIMA model. Finally, the DLSI model is applied to scene classification in variable bit rate (VBR) MPEG video to provide a preliminary indication of potential application.