Volatility modeling of property markets: A note on the distribution of GARCH innovation

Autoregressive heteroscedastic effects in financial time series have been subject to a broad field of applied econometrics. Both academic research, as well as the industry, apply GARCH processes to real estate data with previous investigation mostly focused on securitized real estate positions. So far, the common approach in the literature has been to assume normal distribution of the innovation term for the GARCH modelling of direct real estate markets (Miles, 2008). The specified assumption of normality however falls short of the data characteristics exhibited by direct real estate markets, such as returns of real estate prices explicitly not normally distributed and better characterized by a more leptokurtic, skewed distribution (Schindler, 2009). Ghahramani and Thavaneswaran (2007) point out that typically the innovation distribution is selected without further justification (also see Pin-te & Fuest (2014) footnote for a simple switch to student-t without further justification). Consequently, the omission of a priori assumptions about the innovation term distributions being fit to direct real estate leading to misspecification and -parameterization of GARCH models is the research aim of this study. The employed analysis will utilize monthly transaction-based data for ten US property market subsets, whilst observing a window of time to encompass different market conditions and volatility regimes (Perlin et al., 2021). Determining how ARCH effects might differ across different US real estate submarkets as well as major and non-major markets builds on and extends previous research focused on geographical disaggregation (see Crawford and Fratantoni, 2003; Dolde and Tirtioglu, 1997; Miles, 2008; Schindler, 2009). Subsequently fitting and estimating each data subset with a conditionally normally distributed GARCH model will be juxtaposed by employing a variety of innovation distributions to the data. It follows the central hypothesis of this paper, that the goodness of fit for GARCH models can be improved by allowing for the conditional distribution to be modeled as a flexible a priori assumption. Investigating the differing goodness of fit for the models and employing the most appropriate models to re-estimate the GARCH parameters will allow an analysis of the differences in volatility clustering effects to the model employing normally distributed innovations. The aim is to show empirically, that non-normal innovation term distribution leads to a potentially better goodness of fit of the GARCH model. The utilization of a priori assumptions of GARCH model specification is of high importance not only for portfolio management of investors, but also risk management for economic institutions such as central banks and mortgage banks (Schindler, 2009). To the best of the authors’ knowledge, there is no study which scientifically examines the innovation term distribution of GARCH models of direct real estate investments. This paper aims to provide a better understanding of the influence a priori assumptions of the innovation term can take to increase the validity of volatility models for direct real estate investments.