Integrating Independent Component Analysis and Principal Component Analysis with Neural Network to Predict Chinese Stock Market

We investigate the statistical behaviors of Chinese stock market fluctuations by independent component analysis. The independent component analysis (ICA) method is integrated into the neural network model. The proposed approach uses ICA method to analyze the input data of neural network and can obtain the latent independent components (ICs). After analyzing and removing the IC that represents noise, the rest of ICs are used as the input of neural network. In order to forect the fluctuations of Chinese stock market, the data of Shanghai Composite Index is selected and analyzed, and we compare the forecasting performance of the proposed model with those of common BP model integrating principal component analysis (PCA) and single BP model. Experimental results show that the proposed model outperforms the other two models no matter in relatively small or relatively large sample, and the performance of BP model integrating PCA is closer to that of the proposed model in relatively large sample. Further, the prediction results on the points where the prices fluctuate violently by the above three models relatively deviate from the corresponding real market data

Quantum Brownian motion model for the stock market

It is believed by the majority today that the efficient market hypothesis is imperfect because of market irrationality. Using the physical concepts and mathematical structures of quantum mechanics, we construct an econophysics framework for the stock market, based on which we analogously map massive numbers of single stocks into a reservoir consisting of many quantum harmonic oscillators and their stock index into a typical quantum open system--a quantum Brownian particle. In particular, the irrationality of stock transactions is quantitatively considered as the Planck constant within Heisenberg's uncertainty relationship of quantum mechanics in an analogous manner. We analyze real stock data of Shanghai Stock Exchange of China and investigate fat-tail phenomena and non-Markovian behaviors of the stock index with the assistance of the quantum Brownian motion model, thereby interpreting and studying the limitations of the classical Brownian motion model for the efficient market hypothesis from a new perspective of quantum open system dynamics

Multifractal Behavior of the Korean Stock-market Index KOSPI

We investigate multifractality in the Korean stock-market index KOSPI. The generalized $q$th order height-height correlation function shows multiscaling properties. There are two scaling regimes with a crossover time around $t_c =40$ min. We consider the original data sets and the modified data sets obtained by removing the daily jumps, which occur due to the difference between the closing index and the opening index. To clarify the origin of the multifractality, we also smooth the data through convolution with a Gaussian function. After convolution we observe that the multifractality disappears in the short-time scaling regime $t<t_c$, but remains in the long-time scaling regime $t>t_c$, regardless of whether or not the daily jumps are removed. We suggest that multifractality in the short-time scaling regime is caused by the local fluctuations of the stock index. But the multifractality in the long-time scaling regime appears to be due to the intrinsic trading properties, such as herding behavior, information outside the market, the long memory of the volatility, and the nonlinear dynamics of the stock market.Comment: 12 pages, 4 figures. Physica A, in pres

Agent-based model with asymmetric trading and herding for complex financial systems

Background: For complex financial systems, the negative and positive return-volatility correlations, i.e., the so-called leverage and anti-leverage effects, are particularly important for the understanding of the price dynamics. However, the microscopic origination of the leverage and anti-leverage effects is still not understood, and how to produce these effects in agent-based modeling remains open. On the other hand, in constructing microscopic models, it is a promising conception to determine model parameters from empirical data rather than from statistical fitting of the results. Methods: To study the microscopic origination of the return-volatility correlation in financial systems, we take into account the individual and collective behaviors of investors in real markets, and construct an agent-based model. The agents are linked with each other and trade in groups, and particularly, two novel microscopic mechanisms, i.e., investors' asymmetric trading and herding in bull and bear markets, are introduced. Further, we propose effective methods to determine the key parameters in our model from historical market data. Results: With the model parameters determined for six representative stock-market indices in the world respectively, we obtain the corresponding leverage or anti-leverage effect from the simulation, and the effect is in agreement with the empirical one on amplitude and duration. At the same time, our model produces other features of the real markets, such as the fat-tail distribution of returns and the long-term correlation of volatilities. Conclusions: We reveal that for the leverage and anti-leverage effects, both the investors' asymmetric trading and herding are essential generation mechanisms. These two microscopic mechanisms and the methods for the determination of the key parameters can be applied to other complex systems with similar asymmetries.Comment: 17 pages, 6 figure

Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant

Intertrade duration of equities is an important financial measure characterizing the trading activities, which is defined as the waiting time between successive trades of an equity. Using the ultrahigh-frequency data of a liquid Chinese stock and its associated warrant, we perform a comparative investigation of the statistical properties of their intertrade duration time series. The distributions of the two equities can be better described by the shifted power-law form than the Weibull and their scaled distributions do not collapse onto a single curve. Although the intertrade durations of the two equities have very different magnitude, their intraday patterns exhibit very similar shapes. Both detrended fluctuation analysis (DFA) and detrending moving average analysis (DMA) show that the 1-min intertrade duration time series of the two equities are strongly correlated. In addition, both multifractal detrended fluctuation analysis (MFDFA) and multifractal detrending moving average analysis (MFDMA) unveil that the 1-min intertrade durations possess multifractal nature. However, the difference between the two singularity spectra of the two equities obtained from the MFDMA is much smaller than that from the MFDFA.Comment: 10 latex pages, 4 figure