Reverse mixed data sampling based on expectile regression for inflation at risk and economic growth modeling

This study proposes a Reverse Mixed Data Sampling based on Expectile Regression (R-MIDAS-ER) framework for modeling Inflation at Risk and examining the role of economic growth in inflation risk dynamics. The proposed model addresses two central challenges in macroeconomic risk modeling: the mixed-frequency structure between monthly inflation and quarterly macroeconomic indicators, and the need to capture heterogeneous effects across the conditional inflation distribution. By integrating the Reverse MIDAS structure with asymmetric least squares expectile estimation, the model enables low-frequency real-sector information, particularly quarterly GDP growth, to explain high-frequency monthly inflation without imposing artificial aggregation or interpolation. Numerical experiments are conducted under Gaussian, heavy-tailed, skewed, contaminated, and heteroskedastic residual scenarios to evaluate finite-sample performance and robustness. The results show that R-MIDAS-ER provides stable recovery of the mixed-frequency transmission mechanism and achieves competitive or superior expectile forecasting performance, especially in upper-tail inflation risk regions. The empirical application to Indonesian data from January 2001 to June 2024 further demonstrates that inflation, GDP growth, financial stress, and financial conditions exhibit asymmetric and heavy-tailed behavior, supporting the use of distributional modeling. The R-MIDAS-ER model identifies several historically meaningful high-risk inflation episodes and reveals that GDP growth has a stronger association with upper-tail inflation risk than with lower-tail conditions. Financial conditions also exhibit asymmetric effects across expectile levels. Overall, the proposed framework offers an interpretable and distribution-sensitive approach for monitoring inflation vulnerability in mixed-frequency macroeconomic environments.