Importance of the innovation term for GARCH modelling of direct real estate returns

ABSTRACT

The autoregressive heteroscedastic effects of the conditional volatility processes of direct real estate (capital value) returns are subject to a broad range of econometrics. However, while many specifications have been utilised in the empirical design, the literature has commonly modelled the innovation term within the GARCH volatility processes of real estate capital values through a Gaussian normal distribution. This a priori assumption falls short of the data characteristics exhibited by capital value returns, implying that capital value returns cannot be adequately modelled without adapting to the innovation term distribution. Misspecification can underestimate risk and lead to the over-allocation of riskier assets. This study investigates the impact of the a priori assumption about the innovation terms applied to capital value returns, as well as their robustness, through a time-varying framework. The main findings are that misspecification and parameterisation occur when assuming the normality of the innovation term, and that the application of a priori assumptions of the innovation term beyond those of a normal, Student’s t, or generalised error distribution currently employed in the literature can increase the validity of volatility models when applied to capital value returns. The application of the Johnson – SU distribution yields the best overall performance.

KEYWORDS:

• Capital value returns
• GARCH innovations
• univariate volatility modelling
• risk management
• commercial real estate

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data supporting the findings of this study are available from the corresponding author, K. F. K. Upon reasonable request.

Notes

^1. Granger and Ding (1995) listed a few more such features for financial assets.

^2. Submarkets here refer to the dimension of geographical association for centrals and suburban business district and market size for major and non-major markets.

^3. See Begiazi and Katsiampa (2019) for a list of the relevant model types applied to house price volatility.

^4. See K. Case and Shiller (1987) and Stephens et al. (1995).

^5. The Commercial Business District and Suburban Business District are referred to as CBD and SBD respectively from this point onwards.

^6. For further information regarding the methodology of the please see Geltner and Pollakowski (2007).

^7. Properties not included in this time frame might never play a role in investment universe relevant to investors.

^8. The upper and lower IQR are computed by respectively adding and subtracting the interquartile range to the 75^th and 25^th percentile of the return distribution.

^9. Additional tests for normality are available upon request.

^10. The series was selected due to statistical aggregation potentially diluting volatility structures of individual series. The stylised facts are nonetheless present and observable.

^11. We used the rugarch package (Ghalanos, 2022) as it provides additional conditional densities which have been shown to perform well for other financial assets (Cayton & Mapa, 2012), relative to the fGARCH (Wuertz & Chalabi, 2022). The Johnsons SU distribution was reparametrised from the gamlss package (Rigby & Stasinopoulos, 2005). The skewed variations of the innovations are based on the transformations described in Fernández and Steel (1998) and Ferreira and Steel (2006).

^12. Shibata and Hannan-Quinn are available upon request.

^13. Note: Some properties of GARCH processes, such as the stationarity conditions, make no use of the innovation distribution (Klar et al., 2012).

^14. Results for BIC selection can be made available on request.

^15. The results for the other series of the dataset are congruent with those presented and are available upon request.

^16. The Student’s t-distribution is never selected in the rolling sample across all series and the normal Gaussian only 6 times.

^17. The authors acknowledge a survivorship bias given that only the best performing innovation distribution is selected and no relative performance for the entire dynamic sampling estimation could be obtained.

^18. The other series of the dataset display results congruent with those presented and are available upon request.

Additional information

Funding

The authors state that this research did not rely on external funding from any funding agencies.

Notes on contributors

Karl-Friedrich Keunecke

Karl-Friedrich Keunecke is a PhD student at the International Real Estate Business School at the University of Regensburg, Germany. He received a bachelor’s degree in Politics, Philosophy, and Economics from the University of York, England, and a Master of Science in Real Estate from the University of Regensburg, Germany. He is a study manager and lecturer at the IREBS Real Estate Academy in Munich. His academic work focuses on modelling risk in direct and capital real estate markets.

Cay Oertel

Cay Oertel is a risk controller at IntReal International Real Estate Kapitalverwaltungsgesellschaft mbH (Hamburg, Germany) received a bachelor’s degree in Economics and a Master of Science in Real Estate from the University of Regensburg, Germany. His PhD thesis was titled Risk Management in International Real Estate and Capital Markets. His academic work focuses on modelling risk in international real estate markets.