House price modelling of Denmark’s municipalities using vector autoregression and gradient descent

Sammanfattning: In this thesis, a house price evolution equation of Denmark's municipalities is proposed and solved using both an iterative optimization algorithm, and a closed form solution using Vector Autoregression. The quality of the solutions is investigated, analyzed and compared. Focus is put on the accuracy of the generated price predictions and to what degree the model parameters follow expected features from a well describing model, such as distance and population correlation with parameter values. Overfitting is a central problem using the closed form solution method due to the large number of parameters. It is found that the closed form solution performs badly in describing the system and that the iterative method generated much better models. Depending on the initial conditions, the iterative method more accurately captures the expected features and gives price predictions on fours years within 5%. It is also found that the distance between the municipalities has a relatively large importance on the price correlations. The population size is not found to have any noticeable corresponding impact. It is clear that price inflation is a major factor which needs to be more accurately implemented in future work. For example, by exponential inflation adjustment or working with the logarithm of the prices.