Signal processing models for discrete-time self-similar and multifractal processes

The paper discusses and presents results from recent investigation into three problems. (A) Approaches have previously been developed for describing self-similarity in discrete-time random processes using a discrete-time continuous dilation operator. It is shown here that processes self-similar under this construct, called a discrete-time self-similar system (DTSS), are related to prior discrete-time constructs; specifically they can generate asymptotically second order self-similar processes. (B) The advantage of using long-range prediction of long-range dependent processes is tested. It is shown that for combined long-range and short-range prediction for tracking with a sequence that has bounded increments, long range prediction does not offer a significant tracking advantage. (C) It is hypothesized that DTSS systems with a time-varying parameter generates multifractal processes. Empirical results substantiating this surmise are provided.