Emergence of turbulent epochs in oil prices.

• A novel algorithm is presented for estimation of multi-fractals. • The robustness of the algorithm is illustrated with both synthetic and real data. • The estimation makes use of a time frequency analysis to track changes in parameter values. • In the case of commodities it is shown how important events in the marketplace can be seen in the estimation while not visible in classic modeling. • The modeling and approach is important in financial and economic applications as considered here, but should also be important for physical systems that posses long range behavior. Oil price data have a complicated multi-scale structure that may vary with time. We use time-frequency analysis to identify the main features of these variations and, in particular, the regime shifts. The analysis is based on a wavelet-based decomposition and analysis of the associated scale spectrum. The joint estimation of the local Hurst exponent and volatility is the key to detect and identify regime shifting and switching of the oil price. The framework involves in particular modeling in terms of a process of "multi-fractional" type so that both the roughness and the volatility of the price process may vary with time. Special epochs then emerge as a result of these degrees of freedom, moreover, as a result of the special type of spectral estimator used. These special epochs are discussed and related to historical events. Some of them are not detected by standard analysis based on maximum likelihood estimation. The paper presents a novel algorithm for robust detection of such special epochs and multi-fractional behavior in financial or other types of data. In the financial context insight about such behavior of the asset price is important to evaluate financial contracts involving the asset. [ABSTRACT FROM AUTHOR]