Stock Index Prediction Based on Time Series Decomposition and Hybrid Model

The stock index is an important indicator to measure stock market fluctuation, with a guiding role for investors’ decision-making, thus being the object of much research. However, the stock market is affected by uncertainty and volatility, making accurate prediction a challenging task. We propose a new stock index forecasting model based on time series decomposition and a hybrid model. Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) decomposes the stock index into a series of Intrinsic Mode Functions (IMFs) with different feature scales and trend term. The Augmented Dickey Fuller (ADF) method judges the stability of each IMFs and trend term. The Autoregressive Moving Average (ARMA) model is used on stationary time series, and a Long Short-Term Memory (LSTM) model extracts abstract features of unstable time series. The predicted results of each time sequence are reconstructed to obtain the final predicted value. Experiments are conducted on four stock index time series, and the results show that the prediction of the proposed model is closer to the real value than that of seven reference models, and has a good quantitative investment reference value.     

Multifractal properties of Chinese stock market in Shanghai

In this article, we apply three methods of multifractal analysis, partition function method, singular spectrum method and multifractal detrended fluctuation analysis method, to analyze the closing index fluctuations of Shanghai stock market during the past seven years. We have found that Shanghai stock market has weak multifractal features and there are long-range power-law correlations between index series. The shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten. But when the orders of partition function increase, the strengths of multifractal increase, the singular spectrums become rougher and the general Hurst exponents decrease. These results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation.     

A DFA approach for assessing asymmetric correlations

Here we propose a method, based on detrended fluctuation analysis, to investigate asymmetric correlations in nonstationary time series. The aim is to show that, for a certain range of time scales, different scaling properties are found if signal trending is either positive and negative. We illustrate the method by selected examples from physics and finance.     

Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies

We present a model of complex network generated from Hang Seng index (HSI) of Hong Kong stock market, which encodes stock market relevant both interconnections and interactions between fluctuation patterns of HSI in the network topologies. In the network, the nodes (edges) represent all kinds of patterns of HSI fluctuation (their interconnections). Based on network topological statistic, we present efficient algorithms, measuring betweenness centrality (BC) and inverse participation ratio (IPR) of network adjacency matrix, for detecting topological important nodes. We have at least obtained three uniform nodes of topological importance, and find the three nodes, i.e. 18.7% nodes undertake 71.9% betweenness centrality and closely correlate other nodes. From these topological important nodes, we can extract hidden significant fluctuation patterns of HSI. We also find these patterns are independent the time intervals scales. The results contain important physical implication, i.e. the significant patterns play much more important roles in both information control and transport of stock market, and should be useful for us to more understand fluctuations regularity of stock market index. Moreover, we could conclude that Hong Kong stock market, rather than a random system, is statistically stable, by comparison to random networks.     

Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil

In this paper, we study the auto-correlations and cross-correlations of West Texas Intermediate (WTI) crude oil spot and futures return series employing detrended fluctuation analysis (DFA) and detrended cross-correlation analysis (DCCA). Scaling analysis shows that, for time scales smaller than a month, the auto-correlations and cross-correlations are persistent. For time scales larger than a month but smaller than a year, the correlations are anti-persistent, while, for time scales larger than a year, the series are neither auto-correlated nor cross-correlated, indicating the efficient operation of the crude oil markets. Moreover, for small time scales, the degree of short-term cross-correlations is higher than that of auto-correlations. Using the multifractal extension of DFA and DCCA, we find that, for small time scales, the correlations are strongly multifractal, while, for large time scales, the correlations are nearly monofractal. Analyzing the multifractality of shuffled and surrogated series, we find that both long-range correlations and fat-tail distributions make important contributions to the multifractality. Our results have important implications for market efficiency and asset pricing models.     

The distribution and scaling of fluctuations for Hang Seng index in Hong Kong stock market

The statistical properties of the Hang Seng index in the Hong Kong stock market are analyzed. The data include minute by minute records of the Hang Seng index from January 3, 1994 to May 28, 1997. The probability distribution functions of index returns for the time scales from 1 minute to 128 minutes are given. The results show that the nature of the stochastic process underlying the time series of the returns of Hang Seng index cannot be described by the normal distribution. It is more reasonable to model it by a truncated Lévy distribution with an exponential fall-off in its tails. The scaling of the maximium value of the probability distribution is studied. Results show that the data are consistent with scaling of a Lévy distribution. It is observed that in the tail of the distribution, the fall-off deviates from that of a Lévy stable process and is approximately exponential, especially after removing daily trading pattern from the data. The daily pattern thus affects strongly the analysis of the asymptotic behavior and scaling of fluctuation distributions. Received 9 August 2000 and Received in final form 28 August 2000     

Analysis of the efficiency and multifractality of gold markets based on multifractal detrended fluctuation analysis

In this paper, we investigate the efficiency and multifractality of a gold market based on multifractal detrended fluctuation analysis. Our evidence shows that the gold return series are multifractal both for time scales smaller than a month and for time scales larger than a month. For time scales smaller than a month, the main contribution of multifractality is fat-tail distribution. For time scales larger than a month, both long-range correlations and fat-tail distribution play important roles in the contribution of multifractality. Using the method of rolling windows, we find that the gold market became more and more efficient over time, especially after 2001. The abnormal points of scaling exponents can also be related to some occasional events. By defining a new inefficiency measure related to the multifractality, we find that the gold market is more efficient during the upward periods than during the downward periods.     

Stock mechanics: Predicting recession in S&P500, DJIA and NASDAQ

Proposed in this paper is an original method assuming potential and kinetic energies for prices and for the conservation of their sum that has been developed for forecasting exchanges. Connections with a power law are shown. Semiempirical applications on the S&P500, DJIA, and NASDAQ predict a forthcoming recession in them. An emerging market, the Istanbul Stock Exchange index ISE-100 is found harboring a potential to continue to rise.     

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.     

A New Look at Calendar Anomalies: Multifractality and Day-of-the-Week Effect

Stock markets can become inefficient due to calendar anomalies known as the day-of-the-week effect. Calendar anomalies are well known in the financial literature, but the phenomena remain to be explored in econophysics. This paper uses multifractal analysis to evaluate if the temporal dynamics of market returns also exhibit calendar anomalies such as day-of-the-week effects. We apply multifractal detrended fluctuation analysis (MF-DFA) to the daily returns of market indices worldwide for each day of the week. Our results indicate that distinct multifractal properties characterize individual days of the week. Monday returns tend to exhibit more persistent behavior and richer multifractal structures than other day-resolved returns. Shuffling the series reveals that multifractality arises from a broad probability density function and long-term correlations. The time-dependent multifractal analysis shows that the Monday returns’ multifractal spectra are much wider than those of other days. This behavior is especially persistent during financial crises. The presence of day-of-the-week effects in multifractal dynamics of market returns motivates further research on calendar anomalies for distinct market regimes.     

基于上证指数高频数据的中国资本市场微观特性研究

以上证指数高频数据为研究对象,基于上涨、平缓和下跌三个市场状态分析我国金融市场的微观特性.通过分析上证指数在不同时间间隔下的概率分布、自相关性和多分形三个特性,发现上证指数对数增量序列存在厚尾、列维非高斯分布特征,且随着时间间隔的增大,收益序列愈收敛于正态分布,其中,下降趋势收敛于正态分布的速度更快,拟合于列维分布的效果更好.最为突出的是,在自相关函数分析中,上证指数的收益率无长期记忆性,而波动率则具有较强的记忆性.同时,波动率的自相关性存在明显的周期性特征,即T=240 min,且在下降趋势时其相关性最高.在以时间增量刻画的多重分形结构中,对于不同的时间序列、时间间隔,由于受投资期限和流动性的影响,三种股市状态的收益率波动存在着短期和长期性的差异.上证指数的总体宏观行为与国际成熟股市较为一致,但在微观特性上仍存在显著差异,其所特有的周期性是投资者的惯性反冲所致,而自相关性函数较之成熟股市衰减较慢,则表明投资者的投资行为更多地受历史信息的影响.     

A multifractal detrended fluctuation analysis (MDFA) of the Chinese growth enterprise market (GEM)

A multifractal, detrended fluctuation approach is used to analyze the growth enterprise market (GEM) in China involving a range of correlations in fluctuations of share prices (fat tail), persistent and anti-persistent states. Our analysis exhibits company-specific multifractal characteristics, which vary among the companies listed in the same industry, e.g., the power-law cross-correlations between computer and electronics sectors. These results may help reduce the risk in complex financial markets.     

Resonances and fluctuations at SPS and RHIC

We perform an analysis of preliminary data on hadron yields and fluctuations within the statistical hadronization ansatz. We describe the theoretical disagreements between different statistical models currently on the market and show how the simultaneous analysis of yields and fluctuations can be used to determine if one of them can be connected to underlying physics. We perform such an analysis on preliminary RHIC and SPS A–A data that includes particle yields, ratios and event-by-event fluctuations. We show that the equilibrium statistical model can not describe the K/π fluctuation measured at RHIC and SPS, unless an unrealistically small volume is assumed. Such a small volume then makes it impossible to describe the total particle multiplicity. The non-equilibrium model, on the other hand, describes both the K/π fluctuation and yields acceptably due to the extra boost to the π fluctuation provided by the high pion chemical potential. We show, however, that both models significantly over-estimate the p/π fluctuation measured at the SPS and speculate for the reason behind this. PACS 25.75.-q; 24.60.-k; 24.10.Pa     

Stock market return distributions: From past to present

We show that recent stock market fluctuations are characterized by the cumulative distributions whose tails on short, minute time scales exhibit power scaling with the scaling index α>3 and this index tends to increase quickly with decreasing sampling frequency. Our study is based on high-frequency recordings of the S&P500, DAX and WIG20 indices over the interval May 2004-May 2006. Our findings suggest that dynamics of the contemporary market may differ from the one observed in the past. This effect indicates a constantly increasing efficiency of world markets.     

A new perspective on quiet Sun magnetism

The Hinode mission has provided us with a new, quantitative view of the magnetism of the quiet Sun. It has revealed that the quiet internetwork areas are blanketed by horizontal fields that appear at first sight to have more flux than the vertical fields resolved on the same 0.3″ size scale. These measurements point to the possibility that the horizontal fields might be the primary source of the “hidden turbulent flux” of the quiet Sun anticipated from Hanle effect depolarization. In this paper, evidence is presented suggesting that the “seething” horizontal fields observed by Harvey in 2007 and the horizontal fields revealed by Hinode are the same phenomenon. Because the seething fields appear to be of uniform fluctuation over the whole disk, the phenomenon is most likely not associated with the dynamo source of solar activity. Thus, the small-scale “hidden turbulent flux” lends support to the notion of a local solar dynamo acting on granular sizes and time scales.     

Ergodicity recovery of random walk in heterogeneous disordered media

Significant and persistent trajectory-to-trajectory variance are commonly observed in particle tracking experiments,which have become a major challenge for the experimental data analysis. In this theoretical paper we investigate the ergodicity recovery behavior, which helps clarify the origin and the convergence of trajectory-to-trajectory fluctuation in various heterogeneous disordered media. The concepts of self-averaging and ergodicity are revisited in the context of trajectory analysis. The slow ergodicity recovery and the non-Gaussian diffusion in the annealed disordered media are shown as the consequences of the central limit theorem in different situations. The strange ergodicity recovery behavior is reported in the quenched disordered case, which arises from a localization mechanism. The first-passage approach is introduced to the ergodicity analysis for this case, of which the central limit theorem can be employed and the ergodicity is recovered in the length scale of diffusivity correlation.     

Not Fully Developed Turbulence in the Dow Jones Index

The shape of the curves relating the scaling exponents of the structure functions to the order of these functions is shown to distinguish the Dow Jones index from other stock market indices. We conclude from the shape differences that the information-loss rate for the Dow Jones index is reduced at smaller time scales, while it grows for other indices. This anomaly is due to the construction of the index, in particular to its dependence on a single market parameter: price. Prices are subject to turbulence bursts, which act against full development of turbulence.     

Contagion effects in a chartist-fundamentalist model with time delays

In this paper two models of speculative markets are developed to study the effects of feedback mechanisms in financial markets. In the first model, a crash market model couples a linear chartist-fundamentalist model with time delays with a log-periodic market index I(t) through direct coupling. Numerical solutions to the model show that asset prices exhibit significant persistence as a result of the coupling to the log-periodic market index. An extension to include endogenous wealth dynamics shows that the chartists benefit from the persistent dynamics induced by the coupling. The second model is a two-asset model represented by a 2-dimensional delay-differential equation. Asset one price exhibits limit cycle dynamics while in the second market asset prices follow stable damped oscillations. The markets are coupled through a diffusive coupling term. Solutions to the coupled model show that the dynamics of asset two changes fundamentally with the price now exhibiting a limit cycle. The stable converging dynamics is replaced with limit cycle oscillations around the fundamental.     

Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA

We utilized asymmetric multifractal detrended fluctuation analysis in this study to examine the asymmetric multifractal scaling behavior of Chinese stock markets with uptrends or downtrends. Results show that the multifractality degree of Chinese stock markets with uptrends is stronger than that of Chinese stock markets with downtrends. Correlation asymmetries are more evident in large fluctuations than in small fluctuations. By discussing the source of asymmetric multifractality, we find that multifractality is related to long-range correlations when the market is going up, whereas it is related to fat-tailed distribution when the market is going down. The main source of asymmetric scaling behavior in the Shanghai stock market are long-range correlations, whereas that in the Shenzhen stock market is fat-tailed distribution. An analysis of the time-varying feature of scaling asymmetries shows that the evolution trends of these scaling asymmetries are similar in the two Chinese stock markets. Major financial and economical events may enhance scaling asymmetries.