High-dimensional mixed-frequency IV regression

The technological progress over the past decades has made it possible to generate, to collect, and to store new intraday high-frequency time series datasets that are widely available along with the "old" low-frequency data. Indeed, the economic activity occurs in real time and the economic and financial transactions are frequently recorded instantaneously, while the traditional time series data are available at a quarterly, monthly, or sometimes daily frequencies. Ignoring the high-frequency nature of the data leads to the loss of the information through the temporal aggregation and makes it impossible to quantify the economic activity in real time. At the same time, combining the low and the high-frequency datasets allows obtaining more refined measures of the economic activity that can be used subsequently to inform market participants and to guide policies. In this paper, we introduce a novel high-dimensional mixed-frequency instrumental variable (IV) regression suitable for the datasets recorded at different frequencies. The model connects a low-frequency dependent variable to endogenous covariates sampled from a continuous-time stochastic process. Alternatively, the regressor might be sampled from a continuous-space stochastic process encountered in the spatial data analysis or any other stochastic process indexed by the continuum. This leads to the high-dimensional IV regression with a large number of endogenous regressors.