Time series mathematical modeling in volatility clustering context

Abstract

The work considers an issue of volatility evaluation for prices of open-ended mutual investment funds through GARCH and EGARCH-processes. An evident advantage of EGARCH model use over results obtained with GARCH is the possibility to recognize volatility sign. Such effect is achieved by including the function g _t (ε _{t -1}
) at the positive and negative interval ε _t allows the conditional dispersion process to respond asymmetrically to asset price increase and fall. Besides the study contains approaches with evaluation of time series fractal structure. Numerical results of time series predictions with the local approximation of 1^st and 2^nd orders are obtained. The output matrix of parameters B for the local approximation of 2^nd order.