The paper develops an algorithm for making long-term (up to three months ahead) predictions of volatility reversals based on long memory properties of financial time series. The approach for computing fractal dimension using sequence of the minimal covers with decreasing scale (proposed in [1]) is used to decompose volatility into two0dynamic components: specific A (t ) and structural Hµ(t ). We introduce two separate models forA (t ) and Hµ(t ), based on different principles and capable of catching long uptrends in volatility. To test statistical significanceof its abilities we introduce several estimators of conditional and unconditional probabilities of reversals in observed and predicted dynamic components of volatility. Our results could be used for forecasting points of market transition to an unstable state.