We present a new approach on shape preserving estimation of probability distribution and density functions using wavelet methodology for multivariate dependent data. Our estimators preserve shape constraints such as monotonicity, positivity and integration to one, and allow for low spatial regularity of the underlying functions. As important application, we discuss conditional quantile estimation for financial time series data. We show that our methodology can be easily implemented with B-splines, and performs well in a finite sample situation, through Monte Carlo simulations, using a data-driven choice of the resolution level.

Keywords : Conditional quantile, time series, shape preserving wavelet estimation, B-splines, multivariate process.

JEL : C14, C15, C32.

MSC 2000 : 62G05, 62G07, 42C40, 41A15.