In this paper, consideration is given to the assessment of the availability of long-term memory in a time series with variable coefficients that depend on the Markov chain or the continuous Markov process. In the work we succeeded in establishing sufficient conditions for the present of a long-term memory based on a multifractal detrended fluctuation analysis and a Geweke β Porter-Hudak method. A real example is analysed of the Erste Group in the period 07.01.2000 β 23.10.2017, as a result of which it was possible to prove that this company. 
