Direct determination approach for the multifractal detrending moving average analysis

In the canonical framework, we propose an alternative approach for the multifractal analysis based on the detrending moving average method (MF-DMA). We define a canonical measure such that the multifractal mass exponent τ(q) is related to the partition function and the multifractal spectrum f(α) can be directly determined. The performances of the direct determination approach and the traditional approach of the MF-DMA are compared based on three synthetic multifractal and monofractal measures generated from the one-dimensional p-model, the two-dimensional p-model, and the fractional Brownian motions. We find that both approaches have comparable performances to unveil the fractal and multifractal nature. In other words, without loss of accuracy, the multifractal spectrum f(α) can be directly determined using the new approach with less computation cost. We also apply the new MF-DMA approach to the volatility time series of stock prices and confirm the presence of multifractality.

Statistical properties and pre-hit dynamics of price limit hits in the Chinese stock markets

Price limit trading rules are adopted in some stock markets (especially emerging markets) trying to cool off traders' short-term trading mania on individual stocks and increase market efficiency. Under such a microstructure, stocks may hit their up-limits and down-limits from time to time. However, the behaviors of price limit hits are not well studied partially due to the fact that main stock markets such as the US markets and most European markets do not set price limits. Here, we perform detailed analyses of the high-frequency data of all A-share common stocks traded on the Shanghai Stock Exchange and the Shenzhen Stock Exchange from 2000 to 2011 to investigate the statistical properties of price limit hits and the dynamical evolution of several important financial variables before stock price hits its limits. We compare the properties of up-limit hits and down-limit hits. We also divide the whole period into three bullish periods and three bearish periods to unveil possible differences during bullish and bearish market states. To uncover the impacts of stock capitalization on price limit hits, we partition all stocks into six portfolios according to their capitalizations on different trading days. We find that the price limit trading rule has a cooling-off effect (object to the magnet effect), indicating that the rule takes effect in the Chinese stock markets. We find that price continuation is much more likely to occur than price reversal on the next trading day after a limit-hitting day, especially for down-limit hits, which has potential practical values for market practitioners.

Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series

Notwithstanding the significant efforts to develop estimators of long-range correlations (LRC) and to compare their performance, no clear consensus exists on what is the best method and under which conditions. In addition, synthetic tests suggest that the performance of LRC estimators varies when using different generators of LRC time series. Here, we compare the performances of four estimators [Fluctuation Analysis (FA), Detrended Fluctuation Analysis (DFA), Backward Detrending Moving Average (BDMA), and Centred Detrending Moving Average (CDMA)]. We use three different generators [Fractional Gaussian Noises, and two ways of generating Fractional Brownian Motions]. We find that CDMA has the best performance and DFA is only slightly worse in some situations, while FA performs the worst. In addition, CDMA and DFA are less sensitive to the scaling range than FA. Hence, CDMA and DFA remain "The Methods of Choice" in determining the Hurst index of time series.

Detrending moving average algorithm for multifractals

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter θ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward (θ=0), centered (θ=0.5), and forward (θ=1) detrending windows. We find that the estimated multifractal scaling exponent τ(q) and the singularity spectrum f(α) are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.

Detrended fluctuation analysis for fractals and multifractals in higher dimensions

One-dimensional detrended fluctuation analysis (DFA) and multifractal detrended fluctuation analysis (MFDFA) are widely used in the scaling analysis of fractal and multifractal time series because they are accurate and easy to implement. In this paper we generalize the one-dimensional DFA and MFDFA to higher-dimensional versions. The generalization works well when tested with synthetic surfaces including fractional Brownian surfaces and multifractal surfaces. The two-dimensional MFDFA is also adopted to analyze two images from nature and experiment, and nice scaling laws are unraveled.

Cerebral ventricle-brain ratio in monozygotic twins discordant and concordant for schizophrenia

1. Several studies on monozygotic twins discordant for schizophrenia showed that the cerebral ventricle-brain ratio (VBR) was larger in the twins with schizophrenia, as compared with the corresponding normal twins. 2. The results suggest that the difference of the VBR of the discordant twins was larger than that of the concordant twins of schizophrenia. 3. The authors studied the VBR in four monozygotic twin pairs discordant and four monozygotic twin pairs concordant for schizophrenia by computerized tomography. 4. In the discordant twins, all pairs showed that the VBR of the normal twins was smaller than that of the corresponding twins with schizophrenia. 5. The difference of the VBR of the discordant twins and that of the concordant twins of schizophrenia was not statistically different using Mann-Whitney U test. 6. The preliminary results suggest that the VBR enlargement in schizophrenia is not genetically controlled in monozygotic twins either discordant or concordant for schizophrenia. 7. In monozygotic concordant twins, the brain pathology may be heterogeneous.