Multivariate wavelet-based shape-preserving estimation for dependent observations

Abstract

We introduce a new approach to shape-preserving estimation of cumulative distribution functions and probability density functions using the 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. We discuss conditional quantile estimation for financial time series data as an application. Our methodology can be implemented with B-splines. We show by means of Monte Carlo simulations that it performs well in finite samples and for a data-driven choice of the resolution level.