Study On The Some Characters Of Time Series

ABSTRACT: The multiscale detrended fluctuation analysis (MSDFA) are presented for describing the traffic fractal dynamics with a spectrum of scale exponents, a(s), rather than by a model of lumped parameters al and a2in this paper. It shows more details of scale properties and provides a reliable analysis. We also quantify the effects of Weather, traffic peaks and traffic control on exponent spectra a(s). The results indicate clearly that at large scales, the exponents show large volatility and they have their own exponent patterns. In addition, for the effect of traffic control, the scale exponents of traffic control are continuously obviously larger than those without traffic control at small scales. The multiscale DFA method provides new ways to measure the TI series and distinguishes groups in different conditions. These results have been published by SCI journal Fluctuation and Noise Letters on Sep.29,2013.The two methods are also used to investigate long-term correlation (LC) and cross correlation (CC) in the US and Chinese stock markets during2002-2009. We analyze LC and CC behaviors among indices for the same region to determine similarity among six stock indices and divide them into three groups accordingly. We choose S&P500, HSI, and the Shanghai Composite Index as representative samples for simplicity. We find that MSDFA spectra for US stock, HIS, Shanghai Composite show their own behavior respectively. We also find obtain that the value of MSDFA spectra for china mainland stock is greater than the value of MSDFA spectra for US stock, which represents that US stock market show more complex behavior. We obtain detailed multiscale structures and relations for CC between the three representatives.The multiscale weighted multiscale permutation entropy method is proposed (WMPE) based on multiscale weighted multiscale permutation Entropy (MPE) method in the paper. WMPE is different from multiscale permutation entropy (MPE) in the sense that it suits better signals having considerable amplitude information and also succeeding in accounting for the multiple time scales inherent in the financial systems. The WMPE of each US and Chinese stock market points out the necessity of applying permutation entropy on multiple scales and reveals amplitude-coded information contained in the signals and immunity to degradation by noise when m=5-7. Some new conclusions are gotten by the new characteristics we detected in the comparison. WMPE method can distinguish ShangZheng and ShenCheng from these markets and imply that HSI is more similar to the US markets. WMPE moves the fluctuation range of entropy values of different market down differently reflecting more accurate complexity of different stock markets containing amplitude information. Compared WMPE of ShangZheng and ShenCheng with the WMPE of US markets and HSI, US stock market and HSI may have more amplitude information carried by the signals of stock market. Furthermore, compared with MPE, WMPE can reduce the standard deviation which ensures the results more robust. The conclusion that m=7is the best embedding dimension to investigate the WMPE results can be drawn because the WMPE tends to be stable in a certain range and reflects the necessity of investigation on multiscale and advantages of adding different weight, and it can distinguish these markets while reducing the standard deviations of all the markets.