Modeling the urbanization process of China using the methods based on auto-correlation and spectral analysis

China′s urbanization cannot be modeled by the logistic equation,which is followed by the USA′s urbanization process.In order to reveal the features and property of China′s urbanization,the auto-correlation and spectral analysis are employed to make a multifold study on time series of urbanization from 1949 to 2000.(1) An autocorrelation analysis is implemented,and partial autocorrelation function(PACF) has a first order cutoff.This implies that the urbanization process of China possesses a locality: a change in the i-th year only affects that in the(i+1)th year directly,but cannot affect the changes in and after the(i+2)th year.However,the auto-correlation function(ACF) suggests that a change perhaps influence a change ten years later indirectly.(2) An autoregressive analysis is made and an autoregressive moving-average(ARMA) model is built such as Lt=μ+Lt-1+limq→∞∑qj=0φjet-j=0.510+Lt-1+limq→∞∑qj=00.439jet-jwhere Lt is the i-th year's urbanization level,e is an innovation or "random shock"(white noise),φ is a parameter,and q the order of moving average.(3) A spectral analysis is made based on the residuals of the logistic model,that is,the logistic trend of urbanization level is removed from the time series,and the result shows that there exists a periodic change behind the trend change.The wavelength(cycle length) is about 30 years.The Hurst exponent of the urbanization data is estimated to interpret the periodic behavior.The value of the Hurst exponent,H=0.37,suggests anti-persistence in the urbanization process of China.Based on the above analyses,the process of urbanization is divided into three parts: random process,periodic process,and trend process.Among the three different components of change in urbanization,trend is a basic process,cycle is an accessorial process,and random change is a complex process.The future of China′s urbanization is hard to be predicted using the common methods because of auto-correlation and random disturbance,so new approaches should be found to conduct a convincing prediction.