Threshold mixed data sampling (TMIDAS) regression models with an application to GDP forecast errors

Abstract

For modeling the threshold effect in parameters of the mixed data sampling (MIDAS) models, this paper introduces a model called threshold mixed data sampling (TMIDAS) regression, which allows for a threshold effect in the relationship between dependent and explanatory variables sampled at different frequencies, and the explanatory variables being sampled at a frequency higher than the dependent variable. We develop the estimation procedure of the proposed model and suggest test statistics for threshold effect and the equal weighting scheme used typically in aggregating higher-frequency data before estimating econometric models. Monte Carlo simulations are conducted to examine the performance properties of the estimation and testing procedures, and compare the forecasting performance of the TMIDAS relative to the Markov-switching (MS-)MIDAS and MIDAS models. Our simulation results point out that the estimation and testing procedures work well in finite samples, and the proposed model has a good forecasting performance. We apply the TMIDAS model to investigate presence and pattern of cyclical bias in quarterly GDP forecast errors, and compare the out-of-sample performance of the TMIDAS relative to the MS-MIDAS and MIDAS models for GDP forecast errors. Both simulation and empirical results demonstrate the usefulness of TMIDAS.