The Detection and Empirical Study of Variance Change Points on Housing Prices &amp;lt;br/&amp;gt;—Taking Wuhan City Commodity Prices as an Example

Huihui Shen

doi:10.4236/jmf.2016.65049

Abstract

Economic system mathematical model often contains multiple variance change points about structure model. In the same mean, we combine the Bayesian method with the maximum likelihood method on the detection of the variance multiple change points. With Bayesian method, we can eliminate extra parameters first, and then use maximum likelihood method to find the change position. So we both can eliminate extra parameters and can avoid the change point on the prior distribution unknown problem. In addition, the benefit of the maximum likelihood method is just needed to find out likelihood density function of the maximal solution in the solution space, thus the variance of multiple change point detection problem is resolved. By making substantial analysis with an example from commodity house prices in Wuhan, three changes of variance are found in all. They correspond to the major structure changes of contemporary property market in Wuhan city. The method is practical and effective as the final results shown. It also has a certain practical significance.

Highlights

With the rapid economic development of modern society, we need to deal with more and more economic and financial problems
The benefit of the maximum likelihood method is just needed to find out likelihood density function of the maximal solution in the solution space, the variance of multiple change point detection problem is resolved
F ( x) dx it can be seen that the variance is sample distribution density function, so the detection and analysis of the variance change point is considered to be the sample density function estimation, and we use the maximum likelihood method to estimate the location of the change point

Summary

Introduction

With the rapid economic development of modern society, we need to deal with more and more economic and financial problems. There are many ways to estimate change point, such as Schwarz information criterion method, Binary segmentation method, Bayesian method, maximum likelihood method, the likelihood ratio test, (weighted) Least square method, nonparametric method, cumulative sum method, etc. The reference [4] is used to detect the existence of the transition point, and doesn’t need to export its complex distribution function, so the use of information criterion to estimate the number and position of changing point is relatively simple. The reference [7] considers the detection problem of variance change point in linear process with long memory. They propose the ratio test to detect the variance change point. For general change point problems, we usually consider the changes on the mean and variance, and under the framework of hypothesis test the population distribution is normal in the model, so change point problem of inference is equivalent to the mean or variance change detection [15]

The Variance Change Point Detection

Bayesian Approach to the Change-Point Problem

MLE of the Change Point

Empirical Analysis

Findings

Interpretation and Discussion

Conclusion