Statistical and nonlinear analyses of return volatility dynamics on energy futures

The energy markets, as important parts of global financial markets, have been regarded as complex nonlinear systems. The researches on the return volatility of energy futures are of great significance for grasping the law of operations and measuring the risks of markets. This paper introduces two novel volatility statistics — volatility two-component range intensity (VTRI) and cumulative volatility two-component range intensity (CVTRI) into energy futures markets to investigate the volatility dynamics of eight important energy futures. These two statistics combine the volatility shortest passage time (or volatility duration) with the volatility maximum change intensity and the volatility cumulative change intensity. Then, some statistical properties including probability distribution and tail power-law distribution of VTRI series and CVTRI series for eight energy futures are studied by some statistical analyses methods. Moreover, various nonlinear analytical methods are used to explore some nonlinear behaviors including correlation behavior, similarity behavior and multifractal property of VTRI series and CVTRI series.

Multi-fractal Behaviors of long term daily relative humidity and temperature observed over Benin synoptic stations (West Africa)

The multifractal structure of daily temperature and relative humidity is investigated in this study. Multifractal Detrended Fluctuation Analysis (MFDFA) method has been applied on data observed from 1967 to 2012 at the six synoptic stations of Benin (Cotonou, Bohicon, Parakou, Save, Natitingou and Kandi). We estimate the generalized Hurst exponent, the Renyi exponent, and the singularity spectrum from the data to quantify the multi-fractal behaviors. The results show that multi-fractality exists in both daily humidity and temperature record at Benin synoptic stations. It shows multi-fractality with the curves of h (q), τ (q) and D (q), depending on the values of q. The comparison of the multifractal properties shows that, at all the synoptic stations, the multifractal strength of the temperature is significantly different from the feature the humidity.For the temperature, among the six study sites, the multifractal strength at Natitingou is largest (∆α = 0.6917). This means that Natitingou is the city in which the multifractal property is strongly observed for temperature. At Parakou the multifractal strength is smallest (∆α = 0.5252), meaning that Parakou is the city in which the multifractal property is weakly observed. At all synoptic stations the multifractal strength are superior to 0.5 (Δα> 0.5) indicating the degree of multifractal in temperature time series.For the relative humidity, multifractal strength is smallest Kandi (∆α = 0.3031). This means that Kandi is the city in which the multifractal property is weakly observed. Furthermore, the multifractal strength of Parakou is largest (∆α = 0.7691) meaning that for the relative humidity, Parakou is the city in which the multifractal property is strongly observed. The geographic distribution of the multifractal strength reflects the role of climate dynamic processes on the multi-fractal behavior of humidity and the distinctiveness of physical processes in Benin.

Comparative Multifractal Detrended Fluctuation Analysis of Heavy Ion Interactions at a Few GeV to a Few Hundred GeV

We have studied the multifractality of pion emission process in16O-AgBr interactions at 2.1 AGeV and 60 AGeV,12C-AgBr and 24Mg-AgBr interactions at 4.5 AGeV, and32S-AgBr interactions at 200 AGeV using Multifractal Detrended Fluctuation Analysis (MFDFA) method which is capable of extracting the actual multifractal property filtering out the average trend of fluctuation. The analysis reveals that the pseudorapidity distribution of the shower particles is multifractal in nature for all the interactions; that is, pion production mechanism has inbuilt multiscale self-similarity property. We have employed MFDFA method for randomly generated events for32S-AgBr interactions at 200 AGeV. Comparison of expt. results with those obtained from randomly generated data set reveals that the source of multifractality in our data is the presence of long range correlation. Comparing the results obtained from different interactions, it may be concluded that strength of multifractality decreases with projectile mass for the same projectile energy and for a particular projectile it increases with energy. The values of ordinary Hurst exponent suggest that there is long range correlation present in our data for all the interactions.

Noise Effect on Multifractal Detrended Fluctuation Analysis Based on Element Enrichment Model

Used of the element enrichment model, the multifractal detrended fluctuation analysis (MF-DFA) is applied to analyze the multifractal property for sequences which were added stochastic noise and spike noise, and then we discuss the noise effect on the scaling exponent. The result shows that the scaling exponent is stable under stochastic noise and spike noise. Forq>0, the influence on the scaling exponent is rather small when the element enrichment model was added stochastic noise, and the difference is getting smaller with the increasing parameterp; When adding spike noise whose strength is from 1.5 times to 2.5 times, the corresponding influence is consistent, it indicates that MF-DFA method has a better noise immunity against stochastic noise and spike noise under given conditions.

MASS MULTIFRACTAL CHARACTERIZATION OF BLOOD VESSEL SYSTEMS

The blood vessel system as measured on kidney1 and placenta arteries2,3 is known to be a non-homogeneous fractal with a distribution of local dimensions. We interpret this distribution as a mass multifractal property and we have therefore examined the average of the masses Mi(r) and their qth moments within boxes of increasing size r. The centers i of the boxes are randomly distributed on the vessels. The generalized dimensions Dq are introduced by taking the average of (Mi(r)/M0)q-1 over the centers i, according to the probability distribution Mi(r)/M0 (M0: total mass of the cluster). Thus, we have determined Dq by calculating <(Mi(r)/M0)q-1>< centers i> ∝ (r/L)(q-1) Dq (L: diameter of the cluster).