Hurst estimation of scale invariant processes with drift and stationary increments

TL;DR

This paper introduces a new method for estimating the Hurst parameter of discrete scale invariant processes with drift and stationary increments, applied to financial data, and compares it with existing methods.

Contribution

It presents a novel estimation technique for the Hurst parameter tailored to DSI processes with drift, enhancing analysis of scale-invariant phenomena.

Findings

The new method effectively estimates Hurst parameters in DSI processes.

Application to Dow Jones indices demonstrates practical utility.

Comparison shows competitive performance with existing methods.

Abstract

The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments inside prescribed scale intervals is introduced and studied. To identify the structure of the process, first we determine the scale intervals, their linear drifts and eliminate them. Then a new method for the estimation of the Hurst parameter of such DSI processes is presented and applied to some period of the Dow Jones indices. This method is based on fixed number equally spaced samples inside successive scale intervals. We also present some efficient method for estimating Hurst parameter of self-similar processes with stationary increments. We compare the performance of this method with the celebrated FA, DFA and DMA on the simulated data of fractional Brownian motion.