Abstract: Housing price-to-income ratio (HPIR)is the measurer of housing affordability,the indicator of bubbles in the real estate market,and one of the important indexes for measuring subjective well-being of citizens. As an important index of measuring whether the housing price matches residents' income,HPIR has distinctive regional characteristics. In view of the lack of space and scale in the current research,the study of the HPIR from the perspective of quantitative geography shows its importance. Taking the HPIR as the measuring indicator,this paper analyses the spatiotemporal pattern,global trends,spatial heterogeneities and correlations of HPIR for 343 prefecture-level cities or above in China from 2004 to 2014 by using the rank-size,ESDA-GIS,gravity center migration and trend surface analysis systematically. The results show as following: The rank-size distribution of HPIR of 343 prefecture-level cities in China is consistent with the Zipf law in each chosen year with a high-rank oriented aggregation feature. What's more,the dispersive power was stronger than the agglomeration power, which decreased the degree of aggregation. Housing price to income ratio has distinctive regional characteristics. There are many cities with high HPIR in China,while the number of cities with low HPIR is less. In 2004,there are 173 cities with higher HPIR (HPIR>4),accounting for half of the total number of the administration cells. In 2014,there are as many as 328 administration cells with higher HPIR,accounting for 95.6% of the total,among them,148 cities are very high (HPIR>6),and 13 cities are extremely high (HPIR>10). The spatial difference of HPIR is significant,which shows a trend of the eastern China > western China > the middle China,and the North > the Central > the South. The differentiation of HPIR in Chinese cities shows a trend of expansion from 2004 to 2014,and the big cities'ratios rise more obviously. The HPIR increases gradually from north to south, and west to east. The gravity centers of residential average price (AP),per capita disposable (PCDI)income and HPIR of 343 prefecture-level cities or above in China are located in the east of regional geometric gravity center, and the trajectory of the gravity centers of HPIR and AP shift to direction of south. The transfer of the gravity center of AP and HPIR in speed and scale is much higher than that of the gravity center of PCDI. In 2004 and 2014, the global Moran's I values of HPIR at prefecture level cities or above in China were 0.279 and 0.313;the Z test value exceeds the critical value of 0.05,the confidence level of 1.96,showing the existence of global spatial autocorrelation characteristics. Based on the spatial autocorrelation between HPIR and per capita living space (PCLS),343 prefecture-level cities are divided into four types,the high-HPIR and high-PCLS area,high-HPIR and low-PCLS area,low-HPIR and high-PCLS area,high-HPIR and low-PCLS area. From the first tier cities to the fifth tier cities,the HPIR shows a downward trend. The HPIR of the five types of city shows an overall trend of expansion,and the largest growth is in the first tier cities and the second tier cities.

Key words: housing price-to-income ratio, ESDA-GIS, spatiotemporal disparity, China