Time-varying quantile single-index model for multivariate responses

We consider simultaneous semiparametric estimation of conditional quantiles for multiple responses using a dynamic single-index structure. Motivated by a financial application, a market factor index is constructed that is shared among different portfolios which results in a more interpretable and efficient model, compared to separately building multiple conditional quantiles. On the other hand, the link functions are allowed to be different across portfolios. The asymptotic normality of the index parameter is established, as well as the convergence rate of the nonparametric functions. Monte Carlo studies demonstrated the advantages of the proposed estimator and an application to financial data is used to illustrate the method.