Threshold mixed data sampling models with a covariate-dependent threshold

ABSTRACT

This paper introduces a threshold mixed data sampling model with a covariate-dependent threshold (TMIDAS-CDT), 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 modelled as a linear function of informative covariates. We develop the estimation procedure for the model, and suggest test statistics for threshold effect, threshold constancy and the equal weighting scheme in aggregating high-frequency data. We conduct Monte Carlo simulations to investigate the performance of the estimation and testing procedures. The simulation results support that the estimation procedure works well in finite samples, and the test statistics have good size and power properties.

KEYWORDS:

• Threshold effect
• mixed data sampling (MIDAS)
• Covariate-dependent threshold
• estimation
• testing

JEL CLASSIFICATION:

• C5
• C12
• C13
• C14
• C22

Acknowledgments

The authors acknowledge the financial support from the National Natural Science Foundation of China (No. 72034003 and 71803072).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Ethical approval

This article does not contain any studies with human participants or animals performed by the authors.

Notes

¹ A more general polynomial function is given by $w_{j,k}({\theta }_k)=w_{j,k}({\theta }_{k,1},{\theta }_{k,2})=\frac{exp({\theta }_{k,1}j+{\theta }_{k,2}{j}^2+\dots +{\theta }_{k,q}{j}^q)}{{\sum }_{j=1}^{m}exp({\theta }_{k,1}j+{\theta }_{k,2}{j}^2+\dots +{\theta }_{k,q}{j}^q)}$. Ghysels, Sinko, and Valkanov (2007) illustrate that,

even with only two parameters, the function is flexible enough to mimic different weighting shapes.:

² We thank an anonymous referee for raising this point with us.

³ A further investigation of this issue for a model with a high dimensional $s_t$ is worthwhile, but it will not be pursued in this paper.

Additional information

Funding

This study is supported by the National Natural Science Foundation of China (No. 72034003 and 71803072).