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.
We propose to use intrinsic time scale based on volume when measuring fractal dimension of financial time series. (Dubovikov, 2004) introduces a new method of measuring fractal dimension which is superior to other methods, including well-known Hurst index in terms of speed of asymptotic. As a downside, estimates obtained with new method, are noisy and hard to predict, which in turn complicates its use in practice. We demonstrate that sampling time-series across volume scale, instead traditional physical time scale, could significantly improve predictability of fractal dimension.
(Published in Russian in “Science in Modern Information Society IV” , Fall 2014, ISBN 978-1-50232-179-4)