The Detection and Empirical Study of Variance Change Points on Housing Prices <br/>—Taking Wuhan City Commodity Prices as an Example

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.

Multiscale quantile segmentation

“…The analysis of serial data with presumably abrupt underlying distributional changes, for example, in its mean, median, or variance, is a long-standing issue and relevant to a magnitude of applications, e.g. to econometrics and empirical finance (Preuss et al, 2015;Shen, 2016;Russell and Rambaccussing, 2018), evolutionary and cancer genetics (Olshen et al, 2004;Liu et al, 2013;Zhang and Siegmund, 2007;Jónás et al, 2016;Futschik et al, 2014) or neuroscience (Cribben and Yu, 2017), to mention a few (see Section 1.4 for a more comprehensive discussion). The present work proposes a new methodology for this task, denoted as Multiscale Quantile Segmentation (MQS) which on the one hand, is extremely robust as it does not rely on any distributional assumption (apart from independence) and on the other hand, still has high detection power with (even non-asymptotic) statistical guarantees.…”