中国城市化水平的自回归与功率谱分析

利用1949~2000年的城市人口比重数据,开展中国城市化过程的自相关和功率谱分析,建立了ARMA (1,q )模型。中国的城市化过程具有1阶自相关特征:上一年的一个变动直接影响下一年,间接影响则可达10年之久。ARMA (1,q)模型表明中国的城市化过程在趋势性上附加有丰富的随机性。对提取趋势之后的序列进行功率谱分析,发现趋势性和随机性的背后隐含一个长度为30年左右的周期波动。根据上述研究,将中国的城市化过程分解为三种变动:趋势性、周期性和随机性。研究结论对发展更为完善的城市化预测方法,以及对指导具有中国特色的城市化建设,都可能具有一定程度的启示意义。

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 L_t=μ+L_t-1+lim q→∞ ∑ q j=0 φ^jε_t-j=0.510+L_t-1+lim q→∞ ∑ q j=0 0.439^jε_t-j where L_t is the i-th year's urbanization level, ε 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.