Modelling house price volatility states in the UK by switching ARCH models

Abstract

This article analyses investment risk in the housing market by examining volatility properties of house prices for the UK. We use both ARCH and GARCH models to estimate price conditional heteroscedasticity and find evidence of a time-varying property in the volatilities of the house price series. We then use the SWARCH model and find there are three volatility states in the price series. Our estimations suggest the UK housing markets are relatively stable and different states do not switch very often. The magnitude of high price volatility is as high as 20.99 times of the low volatility for the older housing market and 14 times of the low volatility for the new housing market. In addition, the older housing market is less efficient than the new housing market, since the impacts of events on the volatility state of the older house prices is more lasting than in new housing market.

Notes

¹ A more detailed description of the regime-switching model can be found Hamilton (1994), pp. 678–681.

² We use the RATS Version 6 software produced by Estima to estimate all the models in our article.

³ The two most commonly used model selection criteria are the Akaike information criterion (AIC) and the SBC, However, the SBC is asymptotically consistent, whereas the AIC is biased toward selecting an overparameterized model. Hence, the SBC is used to decide the number of lag terms in this article.

⁴ The other reason is that the previous SWARCH model research, Hamilton and Susmel (1994), also uses AR(1) specification for the mean return equation.

⁵ The sum of ARCH and GARCH coefficients in both AR(1)-ARCH(2) and AR(1)-GARCH(1, 1) model are larger than one, suggesting these two model are inappropriate for estimating the volatilities of two housing markets. Hence, we choose AR(1)-ARCH(1) to estimate switching of the ARCH model, i.e. AR(1)-SWARCH(3, 1) model.