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 (#em/em#+1)th year directly, but cannot affect the changes in and after the (#em/em#+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+lim q→∞ ∑ q j=0 φjεt-j=0.510+Lt-1+lim q→∞ ∑ q j=0 0.439jεt-j where Lt is the #em/em#-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.
CHEN Yan-guang
. Modeling the urbanization process of China using the methods based on auto-correlation and spectral analysis[J]. GEOGRAPHICAL RESEARCH, 2007
, 26(5)
: 1021
-1032
.
DOI: 10.11821/yj2007050019
[1] Batty M, Longley P A. Fractal Cities: A Geometry of Form and Function. London:Academic Press,1994.
[2] 陈彦光.中国的城市化水平有多高？城市规划,2003,27(7):12~17.
[3] Allen.P M. Cities and Regions as Self-Organizing Systems: Models of Complexity.Amsterdam:Gordon and Breach Science Pub. ,1997.
[4] Wilson A G.Complex Spatial Systems: The Modelling Foundations of Urban and Regional Analysis. Singapore: Pearson Education Asia Pte Ltd. , 2000.
[5] Clarke K C, Hoppen S, Gaydos L. A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area.Environment and Planning B: Planning and Design, 1997,24: 247~261.
[6] Sanders L, Pumain D, Mathian H, et al. SIMPOP: A mulitiagent system for the study of urbanism.Environment and Planning B: Planning and Design,1997,24(2):287~305.
[7] 冯健.转型期中国城市内部空间重构.北京:科学出版社,2004.
[8] Friedmann J.China's Urban Transition. Minneapolis, MN:University of Minnesota Press, 2005.
[9] Ness G D, Talwar P P(eds. ).Asian Urbanization in the New Millennium.Singapore:Marshall Cavendish Academic,2005.
[10] 陈彦光,刘继生.基于引力模型的城市空间互相关和功率谱分析.地理研究,2002,21(6):742~752.
[11] 陈彦光,刘继生.城市人口分布空间自相关的功率谱分析.地球科学进展,2006,21(1):1~9.
[12] 周一星,于海波.以"五普"数据为基础对我国城镇化水平修补的建议.统计研究,2002,(4):44~47.
[13] Zhou Y X, Ma L J C.China's urbanization levels: Reconstructing comparable time-series data based on the fifth population census. China Quarterly, 2003, 173: 184~204.
[14] Zhou Y X, Ma L J. China's urban population statistics:A critical evaluation.Eurasian Geography and Economics,2005,46(4):272~289.
[15] United Nations.Patterns of Urban and Rural Population Growth.New York: U.N.Department of International Economic and Social Affairs, Population Division, 1980.
[16] Karmeshu. Demographic models of urbanization.Environment and Planning B: Planning and Design,1988,15(1):47~54.
[17] 周一星.城市地理学.北京:商务印书馆,1995.
[18] 陈彦光.城市化:相变与自组织临界性.地理研究,2004,23(3):301~311.
[19] Bennett R J.Spatial Time Series.London: Pion, 1979.
[20] Johnston R J主编.柴彦威,等 译.人文地理学词典.北京:商务印书馆,2004.
[21] Box G E P, Jenkins G M, Reinsel G C.Time Series Analysis Forecasting and Control (3rd ed. ). Beijing: Posts & Telecom Press, 2005.
[22] Box G E P, Jenkins G M, Reinsel G C著.顾岚,等 译.时间序列分析:预测与控制.北京:中国统计出版社,1997.
[23] Watsham T J, Parramore K. Quantitative Methods in Finance.London/Boston: International Thomson Business Press, 1997.
[24] Diebold F X.Elements of Forecasting (3rd ed. ). Mason, Ohio: Thomson/South-Western, 2004.
[25] Berry B J L.Long-Wave Rhythms in Economic Development and Political Behavior.Baltimore: Johns Hopkins University Press, 1991.
[26] Berry B J L, Kim H. Long waves 1790-1990: Intermittency, chaos, and control.In:Kiel L D, Elliott E(eds. ).Chaos Theory in the Social Science: Foundations and Applications. Ann Arbor: The University of Michigan Press, 1996.215~236.
[27] Fourier J著.桂质亮 译.热的解析理论.武汉:武汉出版社,1993.
[28] Bracewell R N.The Fourier Transform and Its Applications (3rd ed. ). New York: McGraw-Hill Companies, Inc. , 2000.
[29] Bak P.How Nature Works: The Science of Self-organized Criticality.New York: Springer-Verlag, 1996.
[30] Feder J.Fractals. New York: Plenum Press, 1988.
[31] Levy J M.Contemporary Urban Planning (7th ed. ).Upper Saddle River, NJ:Pearson/Prentice Hall,2006.
[32] 陈彦光.中国城市发展的自组织特征与判据.城市规划,2006,30(8):24~30.
[33] 陈彦光,罗静.城市化水平与城市化速度的关系探讨——中国城市化速度和城市化水平饱和值的初步推断.地理研究,2006,24(6):1063~1072.
[34] 周一星,曹广忠.改革开放20年来的中国城市化进程.城市规划,1999,23(12):8~13.
[35] 薛凤旋,蔡建明.研究中国城市化理论学派述评.地理研究,1998,17(2):208~216.
