آنالیز فراکتال چندگانه از سقوط بورس
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|15775||2013||8 صفحه PDF||سفارش دهید||4270 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Physica A: Statistical Mechanics and its Applications, Volume 392, Issue 5, 1 March 2013, Pages 1164–1171
We analyze the complexity of rare events of the DJIA Index. We reveal that the returns of the time series exhibit strong multifractal properties meaning that temporal correlations play a substantial role. The effect of major stock market crashes can be best illustrated by the comparison of the multifractal spectra of the time series before and after the crash. Aftershock periods compared to foreshock periods exhibit richer and more complex dynamics. Compared to an average crash, calculated by taking into account the larger 5 crashes of the DJIA Index, the 1929 event exhibits significantly more increase in multifractality than the 1987 crisis.
It is widely accepted that financial markets illustrate strong signs of complex dynamical systems and the distribution of returns of high frequency data follows a power law. In this context, financial time series exhibit non-linear properties and the stylized facts call for long-memory, fat tails and multifractality  and . Particularly for stock exchange time series, fat tails, power-law correlations and multifractality have been documented in a number of cases ,  and . These results are in disagreement with the traditional economic notion which states that markets act in accordance with the Efficient Market Hypothesis (EMH). The majority of the empirical financial studies aimed in identifying long term correlations either in single or multiple time series data , , ,  and . Unlike large and intraday time series data examination, extreme events of stock exchanges have received little attention. In our situation we are interested in investigating the statistical properties of stock exchange indexes during periods of high stress and namely periods of stock market crashes with emphasis given to 1929 and 1987 crashes. Ref.  analyzed similar extreme event impact but on the exchange rate markets, while  for 88 companies that contribute to the S&P 500 index, during the 26-year period 1983–2009, apply time-lag Random Matrix Theory (TLRMT) for each year and show pronounced peaks in TLRMT singular values during the largest market shocks and economic crises: Black Monday, the Dot-com bubble and the 2008 crash. The purpose of investigating market crashes is based on scientific evidence that such complex systems reveal their structure better when they are under stress than in normal conditions. According to Sornette,  “such extreme events express more than anything else the underlying ‘forces’ usually hidden by almost perfect balance and thus provide the potential for a better scientific understanding of complex systems”. Consequently the examination of these specific great crashes will provide an understanding about the dynamics and complexity of the stock exchange markets will assist especially institutional investors to correctly assessed market risk and, also, it will provide to the policy makers the information needed to put in place the appropriate mechanism in encountering future problems. In this vein, the work of Refs.  and , using intraday data, report a correlation between the width of the estimated multifractal spectrum and future price fluctuation, putting the basic for price fluctuations prediction and thus to future crashes. But Ref.  after testing the above statement, with rigorous research, has come to the conclusion that the multifractal nature in the indexes is not a fact but fiction. This result was further supported by analyzing two additional indexes (S&P 500 and NASDAQ) in developed stock markets. Furthermore Ref. , suggest that it is valuable to apply the partition function approach to the multifractal analysis of stocks and indexes and to the possible application of multifractal properties in market forecasting and managing risk, but by using returns series rather than stock prices or indexes. In this paper, we first calculate the market complexity of the two crises and later we divide the total sample into periods before (foreshocks) and after (aftershocks) the crash in an attempt to identify the changes (if any) in the market dynamics and complexity. In addition we analyze three other main crashes and then we calculate the average crash based on all these rare Dow Jones Industrial Average (DJIA) market events. Last we present the generalized Hurst exponent and we provide some concluding remarks.
نتیجه گیری انگلیسی
We investigated the complexity of major stock market crashes. We have observed that temporal correlations are not linear and with the MF-DFA method we have revealed the existence of multifractality in both stock market crashes. Even the shuffled series, removing the time correlations, still exhibit some degree of multifractality. In addition, in order to observe how the market crashes influenced the stock market complexity, we studied their multifractal properties before and after the crisis. We found that the eruptive event (crash) changes the multifractality, which is increased significantly after the crash. The increase of the multifractal degree in the aftershock period, measured by the width of the multifractal spectrum indicates a gain of heterogeneity, signifying a transition from homogeneous to heterogeneous pattern. A comparison of the two aftershock periods and the average crash as appoint of inference shows a greater degree of multifractality for the 1929 aftershock period, meaning a richer and more complex structure. Lastly based on the generalized Hurst exponent we present evidence of failure of the Efficient Market Hypothesis for the two main crashes both for the total sample and especially for the aftershock periods where antipersistence behavior is presented.