Most existing econometric models such as ARCH(q) and GARCH(p,q) take into account heteroskedasticity (non-stationarity) of time series. However, the original ARCH(q) and GARCH(p,q) models do not take into account the asymmetry of the market's response to positive and to negative changes. Several heuristic modifications of ARCH(q) and GARCH(p,q) models have been proposed that take this asymmetry into account. These modifications turned out to be very adequate and efficient in describing the econometric time series. In this paper, we propose a justification of these heuristic modifications -- and thus, an explanation of their empirical efficiency.