A New Structure for Analyzing Discrete Scale Invariant Processes: Covariance and Spectra

作者：Modarresi N; Rezakhah S^*

来源：Journal of Statistical Physics, 2013, 153(1): 162-176.

DOI：10.1007/s10955-013-0799-4

• Discrete scale invariance
• Wide sense Markov
• Multi-dimensional self-similar process
• Spectral density matrix

Improving the efficiency of discrete scale invariant (DSI) sequence, we consider some flexible sampling of a continuous time DSI process on positive real line with scale greater than one. This sampling has the advantage to have a corresponding multi-dimensional self-similar process. This enables us to obtain spectral representation of such sampled DSI process and corresponding spectral density matrix. By imposing wide sense Markov property on the DSI process, we show that the covariance function and the spectral density matrix are characterized by variances and covariances of adjacent samples in the first scale interval. Finally we present an example as simple Brownian motion and provide its simulations to clarify this study. We also study the performance of this structure on the S%26P500 indices for some special period too.

• 出版日期2013-10