Prediction Of Tianjin Real Estate Market By GARCH And COPULA

Real estate, deciding the level of living quantity, is the base of people's livingand the key industry of national economy. It plays an important role in modern socialactivity. Housing price in most cities has been rising since 2000. It is interesting forgovernment, enterprize and people whether the price will go on rising and what extentit reach. Housing price and take-up areas are the two crucial indicators of real estatemarket. Invariant rule is found from changing data. Time series model is established topredict probability distribution of the two indicator of Tianjin in the future.Prediction generally requires stationary series. Daily average housing price ofurban and city in Tianjin and take-up areas from March 20, 2005 to October 31, 2007were test for stationary by unit-root test through logarithm return. ARMA-GARCHmodel was guaranteed among lots of models by independence test, surrogate data testand conditional heteroscedasticity test. The order of the model will in?uence forecaste?ect. Suitable order was made out by information criteria and testing independence ofresiduals. Parameters were estimated by maximum likelihood.Forecasting price and area's distribution dependents on residuals'distribution.Their extreme behavior is paid more people's attention, so tail distribution was obtainedby generalized Pareto distribution(GPD). The rest was modeled by normal distribution.In order to know joint probability distribution, Copula is needed. Appropriate Copulawas selected from 40 kinds of Copula by maximum likelihood function. Three tail de-pendence coe?cients, measuring the probability of one indicator appearing large valueconditioning another have large value, were computed.Always a number is predicted. But daily price and area must exit stochastic viola-tion, so probability distributions in the future 200 days were predicted by Monte Carlo.Pseudo random numbers, generated from fitted Copula, were transformed according tofitted tail and non-tail quantile function. Mean and deviation of predicted return weregot by fitted ARMA-GARCH model. Raw price and area were calculated through re-versing mean plus deviation times Pseudo random numbers. The empirical distributionof 1000 repeated simulations was regarded as underlying distribution. Mean, median,80% VaR and 95% VaR were estimated. The data from November 1, 2007 to December26, 2007 testified the validity of the prediction results.