Cointegration in a MIDAS Regression

ABSTRACT Mixed data sampling (MIDAS) cointegration models are used to analyse variables observed at different frequencies. In this paper, we start from an assumed autoregressive distributed lag (ADL) model for high‐frequency observations, and derive the resulting representation when the dependent variable is only observed at a lower frequency. We propose a test for cointegration, exploiting knowledge of the implied moving average process in the MIDAS model, and derive its asymptotic null distribution. We study the size and power of the test using Monte Carlo simulations, and illustrate our method using the US annual durables consumption as a function of quarterly GDP.