Introduction
The project aim was to create a model that is capable of predicting the Housing Producer Price Index. The Housing Producer price index is an important measure as it reflects the price changes overtime that builders face for materials, labor and other essentials involved in housing construction. When the housing PPI increases, it reflects a rising cost in housing production, thus meaning higher prices for home buyers as well. Accurate prediction of Housing PPI helps professionals estimate construction cost, and investors forecast market trends.

Methodology

To build the model, an ARIMAX(Autoregressive integrated moving average with exogenous variables) model was used. The ARIMAX is capable of effectively capturing the linear relationship in our data and takes into account the historical patterns as well as factoring in external economic factors. However it does not capture the complex non-linear interactions that can have an impact on Housing PPI. Therefore, a XGBoost machine learning algorithm was also implemented with the ARIMAX. XGBoost is able to capture the non-linear patterns by learning from ARIMAX residual errors. By combining the two models and using a hybrid model, we are able to leverage the ARIMAX linear predictive power and XGBoost flexibility in capturing the non-linear relationship.

The results of the hybrid model produced a training RMSE of 0.65 and a test RMSE of 0.7. The RMSE results suggest that the model was able to generalised well to unseen data. The model also outputted a R-square result of 0.92 on the test set. Indicating that the