Multifractal structure analysis of the numbers of tourist after the Wenchuan Earthquake: Jiuzhai Valley as a case example.

In recent years,a number of methods for forecasting the tourism market have been presented.These methods,which are valuable tools for understanding the stationary fluctuation of tourism systems,include the time series method,the econometric method,the artificial neural network and genetic algorithms.Multifractal detrending moving average method(MF-DMA) is a new nonlinear algorithm,which is usually used to analyze a one-dimensional multifractal or higher-dimensional multifractals. In our research,MF-DMA has been successfully used to characterize the temporal fluctuations in the number of daily domestic and foreign tourists in the Jiuzhai Valley in China.The examined data sets correspond to the number of daily Jiuzhai Valley tourists for the time period of January 1,2007,to December 31,2010.These data are provided by the Jiuzhai Valley Administration.We disaggregate the data into two time series for domestic and foreign tourists.The lengths of data are all 1460.They show that Jiuzhai Valley tourism markets are characterized by long-term memory and are multifractal in nature.We note that the multifractal spectra extracted from the two time series are slightly different.Multifractality is stronger in the foreign tourists' time series than in the domestics'.This means that the influx of foreign tourists is less linear and predictable than that of domestic tourists.To study the contributions of the long-range correlation on multifractality,we destroy the temporal correlations by randomly shuffling the original time series.After this shuffling procedure,what remains are data with exactly the same fluctuation distributions but without memory or correlation.It is shown that the strength of multifractality in the randomly shuffled time series is much smaller than that of the original time series.This shows that the inherent long-term correlation structures in both time series are the main origins of multifractality. In addition,the major sources of multifractality are studied.Based on the sliding window concept,the time evolutions of the multifractal behavior of domestic and foreign tourists are analyzed and the influence of the Wenchuan earthquake on the Jiuzhai Valley tourism system dynamics are evaluated quantitatively.This study indicates that although the Jiuzhai Valley tourism system was seriously affected by the Wenchuan earthquake,the inherent dynamical mechanism of the tourism system has not fundamentally changed over the long term.By May 12,2009,the Jiuzhai Valley tourism system's fractal mechanism had gradually restored to its pre-earthquake state.This means that the Jiuzhai Valley tourism system has the ability to recover in a short time period.Through an in-depth analysis of this phenomenon,we found the critical particle effects on the post-disaster restoration and reconstruction of tourist attractions: a phase transition of quantitative change to qualitative change for tourism market post-disaster recovery,which has fractal characteristics.In the evolution of the tourism system,two key elements play a decisive role: whether to enter a critical state,and the main events that lead to phase transitions.