In the recent years there has been an explosive increase in the number of research papers using machine learning methods for forecasting. In this work, I will focus on comparing the estimation of GDP using classical and machine learning methods. In particular, I am interested in analyzing if the index S\&P 500 can help forecast the GDP, therefore I will take as a basis a work where a VAR model is used to analyze the relationship between GDP and S\&P 500. From there I use three recently developed implementations of the gradient boosting decision tree to model GDP and S\&P 500. The recent implementations are XGBoost, LightGBM and CatBoost and are very famous because they are widely used in winner solutions in Kaggle competitions. The metric I use to do the comparisson is the Mean Squared Error and by using the three machine learning algorithms, I find that they provide better results than the Vector Autoregressive. I also perform grid search with several parameters, taking into account regularization, to avoid overfitting and obtain the lowest mean squared error. To select the best model I consider the evaluation results along with the overfitting measure and finally I take a look to the prediction charts of all the algorithms. In my opinion XGBoost offers the best predictions in this exercise.
