A Study on the Identification Loss in GARCH-MIDAS Models

The aim of this research is to study the identification properties of the GARCH-MIDAS model, introduced by Engle, Ghysels, and Sohn (2013). Since there is no formal research outcome that the specific model suffers from identification problems, its small estimated parameter values suggest this suspicion. To verify this notion, we estimate three distinct GARCH-MIDAS models with stock market and macroeconomic data to check the range of the estimated parameter values. It is found that two out these models possibly suffer from identification issues, due to their small t-statistic values. Next, to formally verify their identification issues, a Monte Carlo simulation study is performed according to the methodology of Andrews and Cheng (2012). Through this simulation, it is found that the GARCH-MIDAS model suffers from identification issues, and new critical values should be computed to make valid inferences from the model. Nevertheless, the new robust critical values, namely the Least Favorable and the Type-I critical values, do not solve the identification problems in the two models and create identification issues to the third model as well.