An investigation of Forex market efficiency based on detrended fluctuation analysis: A case study for Iran

The efficient market hypothesis (EMH) states that asset prices fully reflect all available information. As a result, speculators cannot predict the future behavior of asset prices and earn excess profits at least after adjusting for risk. Although initial tests of the EMH were performed on stock market data, the EMH was soon applied to other markets including foreign exchange (FX). This study uses the detrended fluctuation analysis (DFA) technique to test 01:12:2005–18:04:2010 Iranian Rial/US Dollar exchange rate time series data to see if it can be explained by the weak form of the EMH. Moreover, to determine changes in the degree of inefficiency over time, the whole period has been divided into four subperiods. The study shows that the Iranian Forex market (the Rial/Dollar case) is weak-form inefficient over the whole period and in each of the subperiods. However, the degree of inefficiency is not constant over time. The findings suggest that profitable risk-adjusted trades could be made using past data.     

Detrending fluctuation analysis based on high-pass filtering

Detrended fluctuation analysis (DFA) is a scaling method commonly used for detecting long-range correlations in non-stationary time series. The DFA method uses a trend based on polynomial fitting to extract and quantify fluctuations at different time scales. Basically, such procedure acts as a (non-dynamical) high-pass filter that removes time series components below a given time scale. As an alternative to the polynomial fitting approach, this paper proposes a DFA method based on well-known high-pass filters (e.g., Butterworth, elliptic, etc.). Numerical results show that the proposed DFA approach yields results similar to traditional DFA method. Maybe, the main advantage of the proposed DFA method is that efficient implementations of high-pass filters are available commercially.     

Complexity of Body Movements during Sleep in Children with Autism Spectrum Disorder

Recently, measuring the complexity of body movements during sleep has been proven as an objective biomarker of various psychiatric disorders. Although sleep problems are common in children with autism spectrum disorder (ASD) and might exacerbate ASD symptoms, their objectivity as a biomarker remains to be established. Therefore, details of body movement complexity during sleep as estimated by actigraphy were investigated in typically developing (TD) children and in children with ASD. Several complexity analyses were applied to raw and thresholded data of actigraphy from 17 TD children and 17 children with ASD. Determinism, irregularity and unpredictability, and long-range temporal correlation were examined respectively using the false nearest neighbor (FNN) algorithm, information-theoretic analyses, and detrended fluctuation analysis (DFA). Although the FNN algorithm did not reveal determinism in body movements, surrogate analyses identified the influence of nonlinear processes on the irregularity and long-range temporal correlation of body movements. Additionally, the irregularity and unpredictability of body movements measured by expanded sample entropy were significantly lower in ASD than in TD children up to two hours after sleep onset and at approximately six hours after sleep onset. This difference was found especially for the high-irregularity period. Through this study, we characterized details of the complexity of body movements during sleep and demonstrated the group difference of body movement complexity across TD children and children with ASD. Complexity analyses of body movements during sleep have provided valuable insights into sleep profiles. Body movement complexity might be useful as a biomarker for ASD.     

An approach to generate deterministic Brownian motion

We propose an approach for generation of deterministic Brownian motion. By adding an additional degree of freedom to the Langevin equation and transforming it into a system of three linear differential equations, we determine the position of switching surfaces, which act as a multi-well potential with a short fluctuation escape time. Although the model is based on the Langevin equation, the final system does not contain a stochastic term, and therefore the obtained motion is deterministic. Nevertheless, the system behavior exhibits important characteristic properties of Brownian motion, namely, a linear growth in time of the mean square displacement, a Gaussian distribution, and a −2 power law of the frequency spectrum. Furthermore, we use the detrended fluctuation analysis to prove the Brownian character of this motion.     

电子商务中人类活动的标度行为实证研究

应用去趋势波动分析法,对电子商务中人类网上购物行为进行研究,首次探讨了人类浏览及购买行为时间序列(数量波动)标度律.首先,研究发现人类网上购物行为呈现出明显的周期性,其时间序列的概率密度函数具有显著的双模态特征.其次,利用傅里叶变换方法分析浏览以及购买行为时间序列的功率谱,发现其演化过程不同于无关联的泊松过程.最后,基于功率谱过滤周期性趋势的影响,对去除周期趋势后的浏览和购买行为时间序列进行去趋势波动分析,发现其标度行为表明其具有较强的长程关联特性,且平均标度值近似为1,表明其具有自组织临界性.实证研究结果与其他领域如因特网交通流和金融市场价格波动的标度行为相似,有助于理解人类活动如何影响电子商务系统演化和提高在线商务活动效率,对分析电子商务中人类行为活动的机制和预测其波动趋势具有重要的启示作用.     

Correlation of optical properties with the fractal microstructure of black molybdenum coatings

Coating is commonly used for improving the optical properties of surfaces for solar collector applications. The coating morphology depends on the deposition conditions, and this determines the final optical characteristics. Coating morphologies are irregular and of fractal nature, so a suitable approach for its characterization should use methods borrowed from fractal analysis. The aim of this work is to study the fractal characteristics of black molybdenum coatings on copper and to relate the fractal parameters to the optical properties. To this end, coating surfaces were prepared via immersion in a solution of ammonium paramolybdate for different deposition periods. The fractal analysis was carried out for SEM and AFM images of the coating surface and the fractal properties were obtained with a recently developed high-dimensional extension of the well-known detrended fluctuation analysis (DFA). The most salient parameter drawn from the application of the DFA is the Hurst index, a parameter related to the roughness of the coating surface, and the multifractality index, which is related to the non-linearity features of the coating morphology. The results showed that optical properties, including absorptance and emittance, are decreasing functions of the Hurst and multifractality indices. This suggests that coating surfaces with high absorptance and emittance values are related to complex coating morphologies conformed within a non-linear structure.     

Scaling behavior of earthquakes’ inter-events time series

In this paper, we investigate the statistical and scaling properties of the California earthquakes’ inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events.      

Universal scaling behaviors of meteorological variables’ volatility and relations with original records

Volatility series (defined as the magnitude of the increments between successive elements) of five different meteorological variables over China are analyzed by means of detrended fluctuation analysis (DFA for short). Universal scaling behaviors are found in all volatility records, whose scaling exponents take similar distributions with similar mean values and standard deviations. To reconfirm the relation between long-range correlations in volatility and nonlinearity in original series, DFA is also applied to the magnitude records (defined as the absolute values of the original records). The results clearly indicate that the nonlinearity of the original series is more pronounced in the magnitude series.     

Identification and discrimination of Pseudomonas aeruginosa bacteria grown in blood and bile by laser-induced breakdown spectroscopy

Pseudomonas aeruginosa bacteria colonies have been analyzed by laser-induced breakdown spectroscopy using nanosecond laser pulses. LIBS spectra were obtained after transferring the bacteria from a nutrient-rich culture medium to a nutrient-free agar plate for laser ablation. To study the dependence of the LIBS spectrum on growth and environmental conditions, colonies were cultured on three different nutrient media: a trypticase soy agar (TSA) plate, a blood agar plate, and a medium chosen deliberately to induce bacteria membrane changes, a MacConkey agar plate containing bile salts. Nineteen atomic and ionic emission lines in the LIBS spectrum, which was dominated by inorganic elements such as calcium, magnesium and sodium, were used to identify and classify the bacteria. A discriminant function analysis was used to discriminate between the P. aeruginosa bacteria and two strains of E. coli: a non-pathogenic environmental strain and the pathogenic strain enterohemorrhagic E. coli 0157:H7 (EHEC). Nearly identical spectra were obtained from P. aeruginosa grown on the TSA plate and the blood agar plate, while the bacteria grown on the MacConkey plate exhibited easily distinguishable differences from the other two. All P. aeruginosa samples, independent of initial growth conditions, were readily discriminated from the two E. coli strains.     

Detrended fluctuation analysis of heart intrabeat dynamics

We investigate scaling properties of electrocardiogram (ECG) recordings of healthy subjects and heart failure patients based on detrended fluctuation analysis (DFA). While the vast majority of scaling analysis has focused on the characterization of the long-range correlations of interbeat (i.e., beat-to-beat) dynamics, in this work we consider instead the characterization of intrabeat dynamics. That is, here we use DFA to study correlations for time scales smaller than one heart beat period (about 0.75 s). Our results show that intrabeat dynamics of healthy subject are less correlated than for heart failure dynamics. As in the case of interbeat dynamics, the DFA scaling exponents can be used to discriminate healthy and pathological data. It is shown that 0.5 h recordings suffices to characterize the ECG correlation properties.