Which quantile is the most informative? Markov switching quantile model with unknown quantile level

In this study, we propose a Markov regime-switching quantile regression model, which considers the quantile as an unknown parameter and estimate it jointly with other regression coefficients. The parameters are estimated by the maximum likelihood estimation (MLE) method. Our proposed model aims to address the problem about which quantile would be the most informative one among all the candidates. A simulation study of this proposed model is conducted covering various scenarios. The results show that the MLE method is efficient as the estimated parameters are close to their true values. An empirical analysis is also provided, which focuses on the risk measurement in United States and United Kingdom stock markets. The degree of risk is measured by the most informative quantile regression coefficients in each regime. The result shows that the Markov regime-switching quantile regression model with unknown quantile can explain the behavior of the data better and more accurately than the Markov regime-switching quantile regression model when in terms of the minimum Akaiki information criterion (AIC) and Bayesian information criterion (BIC).