Multi-scale and multi-fractal analysis of pressure fluctuation in slurry bubble column bed reactor

The Daubechies second order wavelet was applied to decompose pressure fluctuation signals with the gas flux varying from 0.18 to 0.90 m3/h and the solid mass fraction from 0 to 20% and scales 1?9 detail signals and the 9th scale approximation signals. The pressure signals were studied by multi-scale and R/S analysis method. Hurst analysis method was applied to analyze multi-fractal characteristics of different scale signals. The results show that the characteristics of mono-fractal under scale 1 and scale 2, and bi-fractal under scale 3?9 are effective in deducing the hydrodynamics in slurry bubbling flow system. The measured pressure signals are decomposed to micro-scale signals, meso-scale signals and macro-scale signals. Micro-scale and macro-scale signals are of mono-fractal characteristics, and meso-scale signals are of bi-fractal characteristics. By analyzing energy distribution of different scale signals,it is shown that pressure fluctuations mainly reflects meso-scale interaction between the particles and the bubble.

Application of long-range correlation and multi-fractal analysis for the depiction of drought risk

By using the multi-fractal detrended fluctuation analysis method, we analyze the nonlinear property of drought in southwestern China. The results indicate that the occurrence of drought in southwestern China is multi-fractal and long- range correlated, and these properties are indifferent to timescales. A power-law decay distribution well describes the return interval of drought events and the auto-correlation. Furthermore, a drought risk exponent based on the multi-fractal property and the long-range correlation is presented. This risk exponent can give useful information about whether the drought may or may not occur in future, and provide a guidance function for preventing disasters and reducing damage.

Modeling and forecasting time series of precious metals:a new approach to multifractal data

We introduce a novel approach to multifractal data in order to achieve transcended modeling and forecasting performances by extracting time series out of local Hurst exponent calculations at a specified scale.First,the long range and co-movement dependencies of the time series are scrutinized on time-frequency space using multiple wavelet coherence analysis.Then,the multifractal behaviors of the series are verified by multifractal de-trended fluctuation analysis and its local Hurst exponents are calculated.Additionally,root mean squares of residuals at the specified scale are procured from an intermediate step during local Hurst exponent calculations.These internally calculated series have been used to estimate the process with vector autoregressive fractionally integrated moving average(VARFIMA)model and forecasted accordingly.In our study,the daily prices of gold,silver and platinum are used for assessment.The results have shown that all metals do behave in phase movement on long term periods and possess multifractal features.Furthermore,the intermediate time series obtained during local Hurst exponent calculations still appertain the co-movement as well as multifractal characteristics of the raw data and may be successfully re-scaled,modeled and forecasted by using VARFIMA model.Conclusively,VARFIMA model have notably surpassed its univariate counterpart(ARFIMA)in all efficacious trials while re-emphasizing the importance of comovement procurement in modeling.Our study’s novelty lies in using a multifractal de-trended fluctuation analysis,along with multiple wavelet coherence analysis,for forecasting purposes to an extent not seen before.The results will be of particular significance to finance researchers and practitioners.