Modelling Housing prices with Non-Causal And Double-Autoregressive Processes with an Exogenous Covariate

Specialeforsvar: Amina Bajric og Frederikke Thuren Schulz


Titel: Modelling Housing prices with Non-Causal And Double-Autoregressive Processes with an Exogenous Covariate


Abstract: This thesis examines whether the bubble structure in housing prices for Capital Region of Denmark, can be modelled, following the work of Gouriérux and Zakoian (2017), which introduces a novel expression for modelling of stochastic processes with "bubbles" or explosive behavior. This new process is a forward-looking non-causal autoregressive process, labelled AR+(q). Inspired by Gourérux and Zakoian (2017), the AR+(1) is reversed in time to achieve the backward-looking double autoregressive process, labelled DAR(1). The analytical time reversion is verified by a simulation study. The DAR(1) process is extended to include an exogenous variable, labelled DAR-X. The empirical analysis consist of two parts. First part examines whether the housing prices for the Capital Region of Denmark can be fitted by the DAR(1) process, gained by the time reversion. The second part examines if the DAR-X process with the long mortgage bond interest rate as covariate, cant the housing prices. Both data sets used for the empirical analysis contain 189 monthly observations, ranging from 2006M01-2021M09. As a basis for the empirical analysis, the properties of the processes are considered, including stationarity and ergodicity, likelihood-based estimation and asymptotic theory of the estimators. Moreover, likelihood-based tests are considered for the processes, where the likelihood-based tests have been developed for the DAR-X process, inspired by Pedersen and Rahbek (2019). After discussing the results, the empirical analysis suggests that the DAR(1) process provides a better _t for the housing price data, than the DAR-X process. These findings suggest that introducing the DAR-X process is redundant since it does not provide additional information to the results obtained from the DAR(1) process.


Vejleder:  Anders Rahbek, Ø.I.
Censor:    Mads Stenbo Nielsen, CBS