2021/02/19 by Ezzedine Mliki, Mliki, Ezzedine, Shaykhah Alajmi +1
Economics, Econometrics and Finance · #Stochastic processes and financial applications #Complex Systems and Time Series Analysis #Financial Risk and Volatility Modeling
paper · pdf · doi:10.48550/arxiv.2102.10166
To extend several known centered Gaussian processes, we introduce a new centered mixed self-similar Gaussian process called the mixed generalized fractional Brownian motion, which could serve as a good model for a larger class of natural phenomena. This process generalizes both the well known mixed fractional Brownian motion introduced by Cheridito [10] and the generalized fractional Brownian motion introduced by Zili [31]. We study its main stochastic properties, its non-Markovian and non-stationarity characteristics and the conditions under which it is not a semimartingale. We prove the long range dependence properties of this process.