Fully nonparametric MIDAS: A new approach for nonparametric mixed frequency time series regression

We introduce Fully NonParametric MIDAS (FNP-MIDAS), a new approach for estimating mixed frequency regressions that extends the widely-used MIxed DAta Sampling (MIDAS) group of models to incorporate nonlinear component functions in parsimonious fashion. We present an implementation that handles multiple regressors, allowing MIDAS models to capture nonlinearity in both the weighting of lags and the dependencies between the input and output time series. In the FNP-MIDAS model, all high-frequency lags of a given time series regressor are transformed by the same component function, but rescaled by different magnitudes using MIDAS coefficients. To estimate the parameters of the model, we propose a simple backfitting algorithm that alternates between coefficient estimation and component function estimation at each iteration. For the latter problem, we apply the recently-developed trend filtering method, which allows for local adaptivity without a substantial increase in computational complexity compared to standard spline regression methods. We demonstrate the outperformance of FNP-MIDAS compared to linear MIDAS models by performing experiments on simulated and real-world data, the latter involving the forecasting of urban atmospheric pollution levels using meteorological conditions.