A Wave-Spectrum Analysis of Urban Population Density: Entropy, Fractal, and Spatial Localization

Table 3

Autocorrelation function (ACF) and partial autocorrelation function (PACF) values of Hangzhou’s population density: 1964–2000. As the sample path is not too long, only the first five values are really significant (26^1/2≈5). In time or spatial series analysis, we can judge the nature of series by standard error or by Box-Ljung statistic including 𝑄-statistic and corresponding significance. Generally, it is easier and more visual to use the two standard-error bands shown in the histograms.

Distance (𝑟)	Lag (𝑙)	1964		1982		1990		2000
		ACF	PACF	ACF	PACF	ACF	PACF	ACF	PACF
0.9	1	0.882	0.882	0.878	0.878	0.892	0.892	0.903	0.903
1.5	2	0.757	−0.093	0.753	−0.075	0.773	−0.110	0.796	−0.105
2.1	3	0.626	−0.099	0.622	−0.099	0.656	−0.058	0.683	−0.084
2.7	4	0.496	−0.073	0.486	−0.099	0.532	−0.107	0.571	−0.066
3.3	5	0.365	−0.090	0.359	−0.057	0.410	−0.065	0.462	−0.052
3.9	6	0.253	−0.014	0.246	−0.028	0.292	−0.072	0.339	−0.152
4.5	7	0.142	−0.084	0.142	−0.050	0.177	−0.071	0.216	−0.091