Machine Learning Methods and Time Series: A Through Forecasting Study via Simulation and USA Inflation Analysis

Modern problems in Economics have tremendously benefited from the ever increasing amount of available information. Hence, most of the recent econometric approaches have focused on how to model and estimate relationships between covariates and dependent variables under this high-dimensional scenario. Particularly in the time series context, one usually aims to produce valuable forecasts of the dependent variables. In this paper our main goal is two-folded: i) employ several modern computationally highly intensive Machine Learning (ML) methods for achieving time series forecasting accuracy under a high-dimensional covariates setting; ii) propose a novel variation of the Elastic Net (ENet), the Weighted Lag Adaptive ENet (WLadaENet), which combines the popular Ridge Regression with a regularization method tailored for time series, the WLAdaLASSO (Konzen and Ziegelmann in J Forecast 35:592-612, 2016). To achieve our goal, we carry out Monte Carlo simulation studies as well as a real data analysis of USA inflation with a forecast range from January 2013 to December 2023. In our Monte Carlo implementations, the WLadaENet presents a solid performance both in terms of variable selection when the true model is sparse and in terms of forecasting accuracy even when the model is not sparse and nonlinearities are included. Our approach also performs reasonably well to forecast the USA inflation for different horizons ahead. Since the chosen period includes the Covid-19 crisis, a sub-period analysis is carried out, not leading to a uniformly best forecaster.