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High-dimensional mixed data sampling models with a covariate-dependent threshold

Lixiong Yang,Luyao Ren,Yihang Ye

Published 2025 in Econometric Reviews

ABSTRACT

Abstract. This article introduces high-dimensional mixed data sampling models with a covariate-dependent threshold, which allows for a threshold effect in the relationship between dependent and independent variables sampled at different frequencies and allows for threshold regimes depending on a time-varying threshold being modeled as a linear function of informative covariates. Based on the MCMC technique and linear approximation, we develop a sparse group LASSO (sg-LASSO) estimator of model parameters. We also establish non asymptotic oracle inequalities for the prediction risk, the l1 and l∞ bounds for the parameter estimator and show that these bounds can be translated easily into asymptotic consistency for prediction, estimation, variable selection, and threshold detection. Monte Carlo simulations are conducted to examine the estimation and predictive performance. The simulation results point out that the estimation, prediction, and selection procedures work well in finite samples. The model is illustrated with an empirical application to nowcasting US GDP growth. Our empirical results demonstrate that the proposed model achieves statistically significant gains in GDP nowcasting accuracy by incorporating a threshold effect to capture non linear effects and performing a regime-specific variable selection.

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