Repository logo
 

Quantiles, Expectiles and Splines


Type

Working Paper

Change log

Authors

De Rossi, Giuliano 
Harvey, Andrew C. 

Abstract

A time-varying quantile can be fitted to a sequence of observations by formulating a time series model for the corresponding population quantile and iteratively applying a suitably modified state space signal extraction algorithm. It is shown that such time-varying quantiles satisfy the defining property of fixed quantiles in having the appropriate number of observations above and below. Expectiles are similar to quantiles except that they are defined by tail expectations. Like quantiles, time varying expectiles can be estimated by a state space signal extraction algorithm and they satisfy properties that generalize the moment conditions associated with fixed expectiles. Time-varying quantiles and expectiles provide information on various aspects of a time series, such as dispersion and asymmetry, while estimates at the end of the series provide the basis for forecasting. Because the state space form can handle irregularly spaced observations, the proposed algorithms can be easily adapted to provide a viable means of computing spline-based non-parametric quantile and expectile regressions.

Description

Keywords

asymmetric least squares, cubic splines, dispersion, non-parametric regression, quantile regression, signal extraction, state space smoother

Is Part Of

Publisher

Faculty of Economics

Publisher DOI

Publisher URL