Analysis of the memory structure of financial time series data with rough fractional stochastic volatility (RFSV) approach

Calculation of time-scale volatility data, it is generally taken as a random walk-based approach. However, this approach assumes that the variance is smooth. Contrarily the roughness is an intrinsic characteristic of volatility and should be researched as important parameter in terms of expressing the effects of noise estimations. In general, risk management tools that consider historical volatility have shown deviant consequences in calculating the optimal protection rate with the rough volatility. Financial volatility models have become important in the finance literature, based on martingale, semi-martingal processes and Brownian movements. In these approaches, analyzes by taking into consideration of long-term dependency, memory and stochastic processes have been developing. At the stage of estimation, there are normally been using Gaussian and Log-normal probability density functions. Literature on approaches which use roughness of volatility developed in in recent years. In this context, when there is roughness of volatility, more important questions are testing of the memory structure and examining that what kind of information memory contains. In this research work, we estimated the memory structure of KOSPI index with the method of RFSV. Keywords: Long-range Dependence, Structural Breaks, Spurious Long Memory, Outliers, RFSV, FSV, fBm.