Empirical Analysis of Commercial Housing Sales Based on EARCH(1,1) Model

Since the 1980s, China’s commercial housing market has shown an unprecedented rapid development, and the commercial houses still has a high price. This paper studies the sales rate of commercial housing sales to find an appropriate model, and it analyzes the volatility of the commercial housing market to describe the sustainable development of the commercial housing market. By selecting month data of China’s commercial housing sales from January 2006 to October 2018, this paper uses EViews7.2 and the ARMA Model as the tool in order to establish EARCH(1,1) through the method of quantitative analysis. It is found that the yield of commercial housing sales has obvious cluster, asymmetry and leverage effect, and the impact of adverse news on the commercial housing market is more significant than the impact of favorable news.


Introduction
In recent years, China's development rate has been very rapid, and the people's living standards have also been significantly improved. China's commercial housing market has ushered in an unprecedented period of development especially in the context of the establishment of a comprehensive well-off society.
Many domestic scholars have conducted a lot of researches for the future development prospects of the commercial housing market. Wei Junjia and Zhang Chi [1] (2014) explored the commercial housing in Nanning through the method of cointegration analysis and stationarity analysis. Shi Huiling [2] (2018) used the cross-sectional data of commercial housing sales and GDP in 30 provinces to How to cite this paper: Shen, S.C. and explore the relationship between commercial housing prices and economic development. Zheng Lan [3] (2006) used the VAR model to discuss the transmission effect of monetary policy in the commercial housing market. Tian Tian and Dong Weijuan [4] (2009) studied the impact of macroeconomics on the demand for commercial housing. None of the above documents have studied the volatility of commercial housing market. This paper establishes commodity housing sales rate of return sequence and also makes a series of quantitative analysis of the residual of the model in order to EARCH model. The development status of China's commercial housing sales market is analyzed, and relevant suggestions are put forward as a reference.

ARCH Effect Test
If the random perturbation term of the subject model a t -ARCH(q) [5], the regression equation can be established: The null hypothesis and alternative hypothesis to be tested are: where, n is the number of sample data; R 2 is the determinant of the auxiliary regression formula. When significance level α and degree of freedom q are , the null hypothesis is not accepted, indicating that there is ARCH effect in this sequence. Otherwise, there is no ARCH effect.

EARCH Model
The EARCH model is also called exponential GARCH model, which was proposed by Nelson [6] in 1991. The conditional variance expression of the model is: where the expression of t h is: If 0 ϕ ≠ , the information function is asymmetric. When ϕ is less than 0, leverage is significant.

Skewness
The skewness measures the symmetry of the data. Normal distribution has a

Kurtosis
The kurtosis measures the flatness of the data distribution. The large data distribution at the tail has a large kurtosis value. The normal distribution has a kurtosis value of 3. Its formula is as follows:

Standard Deviation
The standard deviation can reflect the degree of dispersion of the data set, and the calculation formula is as follows:

Data Preprocessing
It can be seen from Figure 1 (commercial housing sales) that the sales volume of commercial housing presents an exponential trend on the whole. The annual December is much larger than the annual January, showing seasonal influence.
And the unit root test is further used ( Table 1).
According to the results in Table 1   processed as follows: two first-order and one seasonal difference were performed on the data, respectively eliminating the exponential trend and seasonal influence of the sequence, so that the new yield sequence obtained does not have the correlation trend and periodic influence, and at this time, the yield sequence is a stationary sequence.
It can be seen from Figure 2 that the sequence R t is stable, and the continuity and clustering of the sequence can be observed.
According to the results in Table 2, the ADF value is −8.295501. At the significance level of 1%, the sequence does not accept the null hypothesis, and the P value is 0. It is believed that there is no unit root in the sequence R t , indicating that the rate of return at this time is a stable time series.

Normality Test
Calculate each statistic for the new sequence, as known in Table 3. Table 3 lists the results of statistics of the return rate of commercial housing sales R t , in which the skewness is −0.488687, less than 0, indicating the existence of left-deviation phenomenon of the return rate sequence. The kurtosis value was 15.75282, while the kurtosis value of the normal distribution was 3, which was much higher than its range value, indicating that the sequence R t had a dis-

ARCH Effect Test
In order to study the relationship within the return sequence R t , ARMA (auto-regressive moving average) model is taken as the main model, ARMA(2,0) was finally determined as the subject model by analyzing the autocorrelation and partial autocorrelation graphs of the yield R t series, as known in Table 4.
Its parameters are estimated as follows: The sequence autocorrelation LM (Lagrange Multiplier) test for the random perturbation term a t of the equation R t obtained a P value of 0.0034, indicating the existence of autocorrelation in the sequence. Next, the author performs the autocorrelation LM test with order 7 on the sequence, as known in Table 5.  It can be seen from Table 5 that the p-value of the seventh-order statistic is 0.0017, less than 0.01, indicating that the random perturbation term a t sequence of the ARMA model has an autocorrelation, and it has the high order ARCH effect, so the return rate sequence R t can build the GARCH model.

Model Recognition
GARCH(1,1) model should be selected to fit the high-order ARCH effect in the yield sequence R t , and other types of ARCH effect models should be fitted. It can be seen from Table 7

Adaptability Test
The ARCH effect test is performed by the sequence in the variance equation to  find out whether this effect has been eliminated. Figure 3 is an autocorrelation and partial autocorrelation test of the standard deviation residual sequence of the EARCH(1,1) model of the sales rate of commercial housing in China.
It can be seen from Figure 3 that the P value is 0.017 when proceeding to the fifth step, and the autocorrelation hypothesis that the significance level is 0.01 standard deviation residual sequence is rejected, indicating that the residual sequence has no ARCH effect. It may be reasonable to establish an EARCH(1,1) model. Next, ARCH effect test can be performed on the residual sequence.
It can be seen from

Conclusion
This paper mainly studies the characteristics of the return rate of commercial housing sales and finds that the return rate sequence has ARCH effect, and