Quantiles, Expectiles and Splines

Giuliano De Rossi and Andrew Harvey

Cambridge Working Papers in Economics from Faculty of Economics, University of Cambridge

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.

Keywords: Asymmetric least squares; cubic splines; dispersion; non-parametric regression; quantile regression; signal extraction; state space smoother. (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
Pages: 29
Date: 2007-02
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
Note: Ec
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Related works:
Journal Article: Quantiles, expectiles and splines (2009)
Working Paper: Quantiles, Expectiles and Splines (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:cam:camdae:0660

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