Innovative methods for modeling of scale invariant processes. Issue 13 (3rd July 2018)

• Record Type: Journal Article
• Authors: Rezakhah, S.; Philippe, A.; Modarresi, N.
• Is Part Of: Communications in statistics. Volume 47:Issue 13(2018)
• Page Start: 3178
• Page End: 3191
• Publication Date: 2018-07-03
• Subjects: Discrete scale invariant processes -- fractional Brownian motion -- hurst estimation -- scale parameter -- self-similar processes.; 62L12 -- 60G22 -- 60G18; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2017.1350273
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: This paper presents some innovative methods for modeling discrete scale invariant (DSI) processes and evaluation of corresponding parameters. For the case where the absolute values of the increments of DSI processes are in general increasing, we consider some moving sample variance of the increments and present some heuristic algorithm to characterize successive scale intervals. This enables us to estimate scale parameter of such DSI processes. To present some superior structure for the modeling of DSI processes, we consider the possibility that the variations inside the prescribed scale intervals show some further self-similar behavior. Such consideration enables us to provide more efficient estimators for Hurst parameters. We also present two competitive estimation methods for the Hurst parameters of self-similar processes with stationary increments and prove their efficiency. Using simulated samples of some simple fractional Brownian motion, we show that our estimators of Hurst parameter are more efficient as compared with the celebrated methods of convex rearrangement and quadratic variation. Finally we apply the proposed methods to evaluate DSI behavior of the S&P500 indices in some period.