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 is used to decompose volatility into two dynamic components: specific and structural. We introduce two separate models for both, based on different principles and capable of catching long uptrends in volatility. To test statistical significance of 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.
Paper develops volatility forecasting model of RUR/USD exchange rate. To forecast volatility we decompose it to components, characterizing fractal structure of financial time series. Using regression analysis we confirm quasi-cyclical time structure for one of the fractal parameter. We then discuss capacity of the method to predict volatility, including forecasting market transition to unsteady state.