Construct comprehensie indicators through a signal extraction approach for predicting housing price crises

Because of the availability of data, we select Beijing, Shanghai, Tianjin, and Chongqing as the research objects. The time span is from 2005Q3 to 2018Q4. Data are obtained from the China Economic Network Statistics Database, China Economic Network Industry Database, Wind Information, and the National Bureau of Statistics. On the basis of existing studies on the real estate market in China, we select 13 economic variables as individual indicators. These include the M2 growth rate, the exchange rate, the SSE Real Estate, the inflation rate, the medium-term and long-term loan interest rates, the ratio of the completed residential investment in real estate enterprises to the completed residential investment in fixed assets, the ratio of residential property sales to the GDP, the ratio of residential area for sales to the completed residential area, the ratio of residential area under construction to the completed residential area, the residential CPI, the funds in place for real estate enterprises, the land transaction price for real estate enterprises, and the GDP growth rate. We integrate the early warning information from those individual indicators into four comprehensive indicators. The reliability of the early warning system for crises in the urban housing market is verified through the in-sample early warning results. In addition, current housing price movements in the four urban housing markets are analyzed through the out-of-sample results and the crisis prediction probability curves.
Because some of the selected individual indicators have both monthly and quarterly data, some individual indicators only have monthly data, and others only have quarterly data, we use quarterly data only in order to ensure the accuracy and reliability of the data. For individual indicators with only monthly data, we adopt the price index conversion method with a fixed base. We first convert monthly chain data to monthly fixed data (with the base period being December 2005), then convert the monthly fixed data to quarterly fixed data (with the base period being 2005Q4), and finally we calculate quarterly year-on-year data. Because the absolute value of the indicator variable is relatively large, in order to facilitate comparison, we convert all indicator variables into relative values of year-on-year or comparison with other variables.
We take the first three policy cycle time periods of China’s real estate market (from 2005Q3 to 2014Q2) as the in-sample time for building an early warning system for urban housing price crises in China. We use the fourth policy cycle time period (from 2014Q3 to 2018Q4) to evaluate the out-of-sample performance of the early warning system for urban housing price crises.

因数据可得性，我们选取北京、上海、天津、重庆作为研究对象，时间跨度为2005年第三季度至2018年第四季度。数据来源于中国经济网统计数据库、中国经济网行业数据库、万得资讯（Wind Information）以及国家统计局。
在既有中国房地产市场研究的基础上，我们选取13项经济变量作为单项预警指标，具体包括：广义货币供应量（M2）增长率、汇率、上证房地产指数（SSE Real Estate）、通货膨胀率、中长期贷款利率、房地产开发企业住宅竣工投资额占固定资产住宅竣工投资额的比重、住宅商品房销售额占GDP的比重、住宅商品房待售面积与竣工住宅面积的比值、在建住宅面积与竣工住宅面积的比值、居住类居民消费价格指数（CPI）、房地产开发企业到位资金、房地产企业土地交易价格以及GDP增长率。我们将上述单项指标的预警信息整合为四项综合指标，并通过样本内预警结果验证了中国城市住房市场危机预警系统的可靠性。此外，我们还通过样本外预警结果与危机预测概率曲线，对四个城市的住房市场当前房价走势进行了分析。
由于部分选取的单项指标同时包含月度与季度数据，部分单项指标仅具备月度数据，其余仅具备季度数据，为保障数据的准确性与可靠性，我们仅采用季度数据。对于仅具备月度数据的单项指标，我们采用固定基期价格指数转换法：首先将月度环比数据转换为以2005年12月为基期的月度定基数据，随后将月度定基数据转换为以2005年第四季度为基期的季度定基数据，最终计算得到季度同比数据。由于指标变量的绝对数值相对较大，为便于对比分析，我们将所有指标变量转换为同比或相对其他变量的相对值。
我们将中国房地产市场的前三个政策周期（2005年第三季度至2014年第二季度）作为构建中国城市住房价格危机预警系统的样本内时间区间，并以第四个政策周期（2014年第三季度至2018年第四季度）对该预警系统的样本外表现进行评估。