一类Schrdinger算子的连续谱测度(英文)

考虑ｌ２（Ｚ）上的离散Ｓｃｈｒｏｄｉｎｇｅｒ算子，其势Ｖｎ是一个由ｋ＋１个符号｛０，１，２，…，ｋ｝构成的序列．证明了它具有纯连续谱．     

INCREASING PROPERTY OF SPECTRUM IN THE VIBRATIONS OF A CYCLIC CHAIN OF MASSES DISTRIBUTED ACCORDING TO THE GTM SEQUENCE

ＩＮＣＲＥＡＳＩＮＧＰＲＯＰＥＲＴＹＯＦＳＰＥＣＴＲＵＭＩＮＴＨＥＶＩＢＲＡＴＩＯＮＳＯＦＡＣＹＣＬＩＣＣＨＡＩＮＯＦＭＡＳＳＥＳＤＩＳＴＲＩＢＵＴＥＤＡＣＣＯＲＤＩＮＧＴＯＴＨＥＧＴＭＳＥＱＵＥＮＣＥＳｈａｎｇＰｅｎｇｊｉａｎ（商朋见）（Ｄｅｐａｒ...     

Segmented inner composition alignment to detect coupling of different subsystems

Inner composition alignment (IOTA) is a recently proposed, permutation-based asymmetric association measure to identify coupling (interrelations) between different subsystems, together with the associated directionality, which is especially designed for very short time series. In this paper, we extended IOTA to investigate the coupling between subsystems for long time series, which is called segmented IOTA (SIOTA). Both global and local degree of couplings can be detected by varying the segment length. SIOTA is then applied to investigate interactions between stock market indices of America and different countries, and obtain many interesting results. Compared to SIOTA, cross-sample entropy is introduced to obtain consistent results. Besides, time-delay SIOTA, modified from SIOTA, is employed to find the best delay time for two time series with missing values.     

Cross-correlations and structures of stock markets based on multiscale MF-DXA and PCA

Based on the daily closing prices of US and Chinese stock markets, we conduct empirical analysis of the cross-correlations and multiscale distances among the US stock markets and China stock markets using the proposed multiscale multifractal detrended cross-correlation analysis method (MSMF-DXA). It is demonstrated that stock markets appear to be far more complex than hitherto reported in the studies using a fixed time scale. In order to identify and compare the interactions and structures of stock markets during financial crisis, as well as in the pre-crisis and post-crisis periods, all the entire samples are divided into four sub-periods. We are thus able to deeply examine the dynamics of linkages among stock markets during different considered periods by MSMF-DXA and principal component analysis technology. The empirical results indicate that both two financial crises cause the increase of international transmission of stock markets, but the global financial crisis and Asian financial crisis lead to different effects in stock markets. It is indicated that the markets are more correlated during global financial crisis compared to Asian financial crisis. The cross-correlations, especially for the markets within different geographic region, increased significantly during the crisis. It is shown that stock markets can be described by the first and second principal component during normal and crisis period, respectively. The results presented in this paper are useful to interpret the multiscale properties of stock markets and describe the dynamics of interactions among considered stock markets.     

Modified DFA and DCCA approach for quantifying the multiscale correlation structure of financial markets

We use multiscale detrended fluctuation analysis (MSDFA) and multiscale detrended cross-correlation analysis (MSDCCA) to investigate auto-correlation (AC) and cross-correlation (CC) in the US and Chinese stock markets during 1997–2012. The results show that US and Chinese stock indices differ in terms of their multiscale AC structures. Stock indices in the same region also differ with regard to their multiscale AC structures. We analyze AC and CC behaviors among indices for the same region to determine similarity among six stock indices and divide them into four groups accordingly. We choose S&P500, NQCI, HSI, and the Shanghai Composite Index as representative samples for simplicity. MSDFA and MSDCCA results and average MSDFA spectra for local scaling exponents (LSEs) for individual series are presented. We find that the MSDCCA spectrum for LSE CC between two time series generally tends to be greater than the average MSDFA LSE spectrum for individual series. We obtain detailed multiscale structures and relations for CC between the four representatives. MSDFA and MSDCCA with secant rolling windows of different sizes are then applied to reanalyze the AC and CC. Vertical and horizontal comparisons of different window sizes are made. The MSDFA and MSDCCA results for the original window size are confirmed and some new interesting characteristics and conclusions regarding multiscale correlation structures are obtained.     

A new method for tolerance estimation of multivariate multiscale sample entropy and its application for short-term time series

Multivariate multiscale sample entropy (MMSE) is a robust method to detect the complexity of multivariate system. It is evaluated for a certain value of tolerance parameter r which is mainly calculated from common acknowledged range. This kind of selection of r is not suitable for short-term time series and may lead to the unreliable detection. To reduce the impact of limited range of r, we apply cumulative histogram method to estimate the range of r. It is data-driven and needs no parameters. Moreover, we use secondary statistics, AvgMMSE and SDMMSE rather than the single value of MMSE to detect the complexity of signals and differentiate them. Several time series, either generated from chaotic or stochastic systems, are analyzed to demonstrate the approach. The core achievement of this experiment is the stability and classification for short-term time series. Then we apply this method to financial time series. Empirical results show that the proposed method is vigorous enough to classify different stock indices over different periods.     

A measure of complexity based on the order patterns

Cumulative Tsallis entropy (CE) is a recently introduced entropy metric to quantify the uncertainty of time series, and its expressions of continuous random variable and discrete random variable are consistents. So far, it has proved to have a good performance in the characteristics of time series. This paper presents a new method to measure the complexity and similarity of systems—cumulative Tsallis entropy based on the dispersion entropy (DCE). It is different from the traditional PE method to simply symbolize the sequence. Instead, the complexity of the system is characterized by focusing on the amplitude information of the time series and considering the influence of past events. We applied DCE to two kinds of simulation data and six global financial time series. The results show that DCE can be used as a diagnostic model to classify global financial data according to regional characteristics, financial background and government policies. In addition, as a classical method of non-stationary time series, we combine the MSE method with DCE to observe the financial market from different time scales and obtain rich intrinsic properties.

     

Multidimensional scaling method for complex time series feature classification based on generalized complexity-invariant distance

Nonlinear Dynamics - In this paper, we propose a multidimensional scaling (MDS) method based on complexity-invariant distance (CID) and generalized complexity-invariant distance (GCID) to analyze...     

The novel multi-scale local irreversibility analysis method based on segmentation about time series

Nonlinear Dynamics - In this paper, we mainly study the local irreversibility of time series. For this purpose, inspired by the idea of segmentation contained in multi-fractal detrended fluctuation...